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Preview of Calculus Worksheet #14: Curve Sketching

Calculus Worksheet #14: Curve Sketching

The 14th of a 20-worksheet sequence created to scaffold and support honors calculus curriculum. Covers finding intervals of increase/decrease and relative extrema; identifying intervals of concavity and points of inflection; and using these to generate accurate graphs of differentiable functions. With a focused and self-contained design, this versatile resource can be used as a small group activity, a homework assignment, a quiz, individual practice for a classwide lesson, or targeted review for
Preview of Analytical Applications of Differentiation (AP Calculus AB - Unit 4)

Analytical Applications of Differentiation (AP Calculus AB - Unit 4)

Created by
Math Lion
Analytical Applications of Differentiation Calculus Unit Bundle:This is a bundle with guided notes, PowerPoints aligned with the guided notes, additional practice (homework), mid-unit quiz, unit test, unit review, and unit pacing guide for Analytical Applications of Differentiation (Unit 4). This unit contains 6 lessons. Lesson 4.1: Using the Mean Value TheoremLesson 4.2: Extrema on an IntervalLesson 4.3: Increasing and Decreasing Intervals and The First Derivative TestLesson 4.4: Concavity and
Preview of Functions - Increasing, Decreasing, Maxima and Minima

Functions - Increasing, Decreasing, Maxima and Minima

This self-checking worksheet has 9 functions which should be put into a graphing utility to find the maximum and/or minimum value. Then, using those values, find either the increasing or decreasing interval. When finished, the students will find a mathematical saying.
Preview of AP CALCULUS AB - 5.9 CONNECTING F(X) WITH ITS 1ST & 2ND DERIVATIVES WORKSHEET

AP CALCULUS AB - 5.9 CONNECTING F(X) WITH ITS 1ST & 2ND DERIVATIVES WORKSHEET

Created by
MATH WITH YOSH
This Calculus worksheet is intended for students after they have learned the 5.9 AP Calculus AB Topic: "Connecting a Function, Its First Derivative, and Its Second Derivative." When given the graph of f', often times my students struggle with identifying where the graph of f has a local minimum or maximum, where f is increasing/decreasing, or identifying where the graph of f is concave up/down, or has a point of inflection. Similarly, when given the graph of f'', they tend to struggle with ide
Preview of Applications of Differentiation Lesson 3 of 7

Applications of Differentiation Lesson 3 of 7

This lesson covers finding extrema on an open interval and the first derivative test (increasing, decreasing and extrema). It also covers given the graph of a function, sketching the derivative.
Preview of Calculus - Curve Sketching Activity Sheet w Spanish Translation

Calculus - Curve Sketching Activity Sheet w Spanish Translation

This activity sheet has 10 conceptually based questions on using information about the first and second derivatives to create a sketch of a function. Students use the first derivative to decide where a function might increase, decrease, or level off. The second derivative describes where the function is concave up or down and where a point of inflection might occur. The questions are designed to be used with Advanced Placement Calculus students. A Spanish translation is included. You will
Preview of AP® Precalculus Unit 3.1 Periodic Phenomena Activity

AP® Precalculus Unit 3.1 Periodic Phenomena Activity

Do you find that your AP ® Precalculus need more practice relating to periodic functions and finding the intervals for increasing, decreasing and concavity? Students will work through six problems to describe how to tell functions are periodic and then to describe the intervals for increasing, decreasing, concave up and concave down. ⭐Skills Required: Writing intervals for increasing and decreasingWriting intervals for concave up and downDetermining functions are periodic or not❤️Resource is Gr
Preview of IB Math SL - Applications of Derivatives Problem Set

IB Math SL - Applications of Derivatives Problem Set

This problem set is for applications of derivatives. The main topics of the notes revolve around increasing/decreasing functions, local minimums and maximums, concavity, points of inflection, kinematics, and optimization.
Preview of Critical Numbers, First and Second Derivatives

Critical Numbers, First and Second Derivatives

Created by
PatrickJMT
Critical Numbers, First and Second Derivatives. In this file, there are problems related to finding critical numbers, intervals of increase / decrease, local maximums and minimums, concavity and inflection points.
Preview of Calculus 1 (AB) Study Guide Formulas Reference Sheet 1 by Cute Calculus

Calculus 1 (AB) Study Guide Formulas Reference Sheet 1 by Cute Calculus

Created by
Cute Calculus
•••If you find this download useful, please rate 5 star!•••Examples, explanations, CALCULUS MADE SIMPLE ON ONE SHEET front and back! Designed by a lover of all things colorful and compulsive doodler, April Terrazas. Designed to print front/back and 3-hole punch. Tutoring available, DM @CuteCalculus•Difference quotient •Average Rate of Change •Constant Rule •Power Rule •Sum/Difference Rule •Constant Rule Multiple •Product/Quotient Rule •Chain Rule •Inverse Function Theorem •Derivatives of Trig F
Preview of AP CALCULUS BC - 7.9 LOGISTIC DIFFERENTIAL EQUATIONS WORKSHEET

AP CALCULUS BC - 7.9 LOGISTIC DIFFERENTIAL EQUATIONS WORKSHEET

Created by
MATH WITH YOSH
This Calculus worksheet is intended for students after they have learned the 7.9 Logistic Models with Differential Equations lesson from Unit 7 (AP Calculus BC Course and Description). In this worksheet, I have included multiple choice practice problems where students apply the model for logistic growth: dy/dt=ky(a-y). Given a logistic differential equation, students will then be able to identify: 1. The limiting value (carrying capacity) 2. The graph of the solution to a logistic differential
Preview of Calculus Summer Assignment

Calculus Summer Assignment

Created by
Idempotent
Self-executing lessons are ideal for sub-plans, as supplemental material for "flipped" classrooms, or for any teacher wanting to leverage their limited instructional time. The learning of basic notation and rules is accomplished via pattern recognition. This self-executing lesson will get precalculus students started learning calculus over the summer so that next year begins smoothly. It would be particularly useful for calculus teachers needing to accelerate the pacing of their curriculum. DA
Preview of Calculus CURVE ANALYSIS Where is f increasing AND concave up? Dec/Conc up? Etc.

Calculus CURVE ANALYSIS Where is f increasing AND concave up? Dec/Conc up? Etc.

Created by
Amy Reed
Calculus CURVE ANALYSIS (Inc/Dec AND Concavity) First & Second Derivative Tests Worksheet consists of 10 different functions. For each of the 10 functions students are asked to find open intervals for which the function is "increasing AND concave down" or "decreasing AND concave up" etc. The functions range from polynomials to functions containing e and ln. Space is provided with each problem for students to write organized justifications for their solutions. I created this practice becaus
Preview of Change in Tandem AP® Precalculus 1.1 Activity Cut and Paste

Change in Tandem AP® Precalculus 1.1 Activity Cut and Paste

Do you find that your AP ® Precalculus need more help on the change in tandem topic? Students will work on identifying the relationship between the input and output for given functions graphically and describe the rate of change as increasing, decreasing, positive and negative for AP ® Precalculus topic 1.1. This activity can be completed as just a worksheet or as a cut and paste activity. Students can cut out the solutions and paste them into the specific box for easy differentation as well.
Preview of Applications of Derivatives: Maximum Velocity of a Cough

Applications of Derivatives: Maximum Velocity of a Cough

This is created to be an in class assignment graded assignment, which will take approximately 25 minutes depending on the skill levels of the students. The answer key/scoring guidelines are attached at the end of the worksheet. The worksheet should be used after Increasing and Decreasing Functions and the First Derivative Test are taught.
Preview of Logarithmic & Exponential Functions: Sort & Match Activity

Logarithmic & Exponential Functions: Sort & Match Activity

Looking for an engaging way to help your students master logarithmic and exponential functions? This hands-on mix-and-match activity is perfect for reinforcing key concepts while making learning fun! Students will: • Sort functions and identify their domain, range, zeros, y-intercept, and more. • Analyze positive and negative intervals, and determine increasing and decreasing behaviors. • Complete a cut-and-paste activity to match functions with their corresponding parts and glue them in orde
Preview of Rational Functions Sort-and-Match Activity | Domain, Range, Asymptotes, and More

Rational Functions Sort-and-Match Activity | Domain, Range, Asymptotes, and More

Rational Functions Sort-and-Match Activity | Domain, Range, Asymptotes, and MoreEngage your high school math students with this interactive Rational Functions Sort-and-Match Activity! This resource is designed to help students master the key characteristics of rational functions, including: • Domain and Range • Zeros • Vertical, Horizontal, and Slant Asymptotes • Increasing and Decreasing Intervals • Y-intercepts • Positive and Negative Intervals • End Behavior What’s Included: • 10 rati
Preview of Complete Curve Analysis – Mastering Function Behavior in High School Mathematics

Complete Curve Analysis – Mastering Function Behavior in High School Mathematics

Curve sketching is more than drawing graphs—it is about understanding how functions behave. Complete Curve Analysis helps students move beyond memorized checklists toward genuine mathematical insight. This classroom-ready resource presents curve analysis as a coherent analytical process. Students explore how the function term, its derivatives, and its limits interact to shape the overall graph. By focusing on reasoning and interpretation, the material enables learners to explain why a funct
Preview of Rates of Change Roller Coaster Activity Practice AP® Precalculus 1.2 and 1.3

Rates of Change Roller Coaster Activity Practice AP® Precalculus 1.2 and 1.3

Do you find that your AP ® Precalculus need more help connecting rate of change to real scenarios? Students will work on describing how two quantities very together and find the average rate of change for AP ® Precalculus topic 1.2-1.3. ⭐Skills Required: Rates of ChangeIncreasing and decreasingRate of change increasing and decreasingConcave up and concave down❤️Resource is Great for: AP® PrecalculusAP® CalculusAlgebra 2Remote LearningHomeschoolingTutoring⭐Includes: 2-page activity (2 versions
Preview of Advanced Curve Sketching Practice — Calculus AB/Calculus 1

Advanced Curve Sketching Practice — Calculus AB/Calculus 1

Transform curve sketching from a memorized checklist into a meaningful reasoning process. This Calculus AB practice packet gives students 10 full curve-sketching problems that build conceptual understanding through progressively challenging function types — polynomial, rational, trigonometric, logarithmic, exponential, and piecewise. Each question leads students through: Domain and range reasoning Continuity and differentiability Critical points and increasing/decreasing intervals Concavi
Preview of Polynomial Functions and Rate of Change AP® Precalculus 1.4 Worksheet

Polynomial Functions and Rate of Change AP® Precalculus 1.4 Worksheet

Do you find that your AP ® Precalculus students need more help connecting average rate of change to graphs and applying key characteristics to polynomial functions? Students will work on describing how two quantities very together and find the average rate of change for AP ® Precalculus topic 1.4. ⭐Skills Required: Rates of ChangeIncreasing and decreasingRate of change increasing and decreasingMaximum and MinimumGlobal, absolute, local, relative❤️Resource is Great for: AP® PrecalculusAP® Ca
Preview of 5 INCR./DECR., RELATIVE EXTREMA, GIVEN F' IDENTIFY CHARACTERISTICS OF F

5 INCR./DECR., RELATIVE EXTREMA, GIVEN F' IDENTIFY CHARACTERISTICS OF F

Created by
MATH WITH YOSH
This Calculus worksheet is intended for students after they have learned the following topics (Unit 5 AP Calculus Course and Description): 5.3 - Determining intervals on which a function is increasing or decreasing 5.4 - Using the first derivative test to determine relative (local) extrema In this worksheet, students will practice given the graph of f', identifying the intervals of increase and decrease of f and where f has a local minimum and maximum. They will also practice given a function f,
Preview of Mega Math Practice Bundle | 111 Printable PDF Worksheets | All K-12 Skills

Mega Math Practice Bundle | 111 Printable PDF Worksheets | All K-12 Skills

TITLE:Mega Math Practice Bundle – 111 Printable Worksheets Covering K–12 Skills Across 10 Topics PRODUCT DESCRIPTION:Unlock the ultimate printable math collection with this all-in-one Mega Math Practice Bundle—a powerhouse set of 111 high-quality PDF worksheets spanning every major math domain from Kindergarten through 12th grade. Organized into 10 expertly crafted topic bundles, this pack delivers thousands of skill-building questions across fluency drills, conceptual practice, and rea
Preview of Calculus Test - Applications of Differentiation

Calculus Test - Applications of Differentiation

Created by
Infinity
This is a 12-question test on Applications of Differentiation that can also be used as homework, review, or self-teaching. * Easel Activity included. Included in this file are: 1. The chapter test with complete, detailed, teaching-oriented solutions. A student could use this to self-teach the concepts. 2. The test with answers only, no solutions. 3. The blank test with room for students' responses. 4. The blank test condensed to two pages, with no room for students' responses. This gives you the
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