Percent Increase and Decrease Quiz
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Increasing, Decreasing and First Derivative Test | Calculus Notes & Video
Increasing, decreasing and First Derivative Test lesson for Calculus with guided notes, homework, and video lesson. Teach intervals of increase and decrease, derivative sign charts, and relative extrema.This is one lesson from my Calculus Unit 3 – Applications of Derivatives curriculum. It includes guided notes, homework practice, a full video lesson, and detailed step-by-step answer keys to support student understanding. This lesson is designed for a guided, non-AP Calculus course and works wel
11th - 12th, Higher Education
Calculus, Math
Differentiation
Apply differentiation to gradients, tangents and normals, increasing
and decreasing functions and rates of change (including connected
rates of change);locate stationary points, and use information about stationary points in sketching graphs (the ability to distinguish between maximum points and minimum points is required, but identification of points of inflexion is not included).
The unit includes:
1) The Limit & Differentiation
2) The Derivative and Tangent Line Problem
3) Basic Differenti
11th - 12th, Higher Education
Calculus, Math, PreCalculus
Calculus - Studying the Behavior of Functions Graphically
Students use the graphing calculator to create graphs of f, f’, and f”, and make observations about conditions that cause f to be increasing f to be decreasing, Extrema to occur A point of inflection based upon information from various graphs. This is a great lesson for students to use prior to knowing all the analytical techniques for taking a derivative. Using the built-in features on the graphing calculator students can graph a derivative of a function and a second derivative of a f
10th - 12th, Higher Education
Calculus, Math
Calculus - Reading and Using Information from the Graph of f'
From a graph of f’ students are asked to describe where f is increasing and decreasing, the locations for all local minimums and maximums for f, locations of all absolute minimums and maximums for f, locations of all points of inflection, and to make a sketch of f and f”.
10th - 12th, Higher Education
Calculus, Math
CALCULUS: LOCAL MAXIMUM AND LOCAL MINIMUM
Objectives:
Upon completion of this section, the student should be able to:
• Use derivatives to determine the intervals of increase and decrease of a given function
• Use the First Derivative Test to determine any local maximum or minimum points
11th - 12th, Adult Education, Higher Education
Applied Math, Calculus
Also included in: BASIC CALCULUS
Graph Analysis Using the 1st Derivative Notes, Examples, Handout, & Assignment
This resource includes notes, examples, and assignment using the 1st derivative to analyze functions. Topics included are: · Critical Numbers · Intervals of Increase and Decrease · Relative Extrema · Absolute Extrema Function types included are: · Quadratic · Cubic · Rational · Trigonometric
11th - 12th, Higher Education
Calculus
Derivatives Graph Analysis Using Tables: Notes, Ex, Handout & Assign (Editable)
This resource includes notes, examples, handout and assignment analyzing graphs of functions using tables. Tables include: · Relative Extrema · Inflection Points · Intervals of Increase and Decrease · Intervals of Concave Upward and Concave Downward · Vertical Asymptotes Students will complete tables with: · Information about f(x) · Information about f'(x) · Information about f''(x) · Description of graph
11th - 12th, Higher Education
Calculus
Derivatives -Graph Analysis Using Tables - Notes, Examples, Handout & Assignment
This resource includes notes, examples, handout and assignment analyzing graphs of functions using tables. Tables include: · Relative Extrema · Inflection Points · Intervals of Increase and Decrease · Intervals of Concave Upward and Concave Downward · Vertical Asymptotes Students will complete tables with: · Information about f(x) · Information about f'(x) · Information about f''(x) · Description of graph
11th - 12th, Higher Education
Calculus
Functions and Their Properties Advanced Math/Pre Calculus Mini Lesson
This SmartBoard mini lesson includes determining if a relation is a function, function notation, implied vs relevant domain, findng the domain and range of a function, continuity and types of discontinuity, increasing and decreasing functions, boundedness, local extrema, even and odd functions, identifying asymptotes,and using limit notation,
10th - 12th, Higher Education
Calculus, PreCalculus
AP® Calculus AB/BC - Unit 5: Analytical Applications of Differentiation
This resource includes one powerpoint-style lesson (example is in the preview) per section, one worksheet set with full solutions per section, one reference sheet for the unit, and one unit test for the unit with solutions. Unit 5: Analytical Applications of Differentiation5.1 The Mean Value Theorem (MVT) and Rolle's Theorem 5.2 Using the First Derivative Test (Increasing/Decreasing, Critical Points) 5.3 Using the First Derivative Test (Relative Extrema) 5.4 Using the Second Derivative Test (Con
12th, Higher Education
Calculus
Also included in: AP® Calculus AB - Full Course Curriculum
AP Calculus: The First and Second Derivative Tests Complete Lesson
This lesson introduces the First and Second Derivative Tests in the context of polynomials. (The lesson on Curve Sketching uses these tests to examine other types of functions.) The lesson begins with a review of increasing and decreasing functions as well as critical numbers. Then, the First Derivative Test is introduced, along with an application. After that, concavity and inflection points are introduced. Finally, the Second Derivative Test is shown, along with an example. This lesson is
10th - 12th, Higher Education
Calculus, Math
Also included in: AP Calculus AB Full Curriculum
AP Calculus: Curve Sketching Complete Lesson
In this lesson, students gain practice in using calculus to understand the features of a graph. Students learn to identify the domain, intercepts, and symmetry of a function. They also practice using calculus to find asymptotes, intervals of increase and decrease, intervals of concavity, local extrema, and points of inflection. This lesson is appropriate for both AP Calculus AB and BC. Detailed answer keys are included. The topics covered include: -Features of a Function -Rational Function -Tr
10th - 12th, Higher Education
Calculus, Math
Also included in: AP Calculus AB Full Curriculum
Calculus - How are the Graphs of f, f ', and f " interrelated?
Using the graphing calculator, students learn how the graphs of the first and second derivatives describe the behavior of the original function. The activity is composed of four parts. Students make observations based upon a series of questions about increasing, decreasing, extrema, and concavity
10th - 12th, Higher Education
Calculus, Math
AP Calculus: Graphing the Derivative Complete Lesson
This lesson helps students learn how to graph the derivative of a function, given a graph of the function. Students also learn how to interpret the graph of the derivative and they make the connection between the derivative of the position function and the velocity function. Increasing and decreasing functions are also introduced. Finally, students learn how to estimate derivatives from a table of values and then use those values to create a graph of the derivative. This lesson is appropriate
9th - 12th, Higher Education
Calculus, Math
Also included in: AP Calculus: Derivatives Unit Bundle
CALCULUS: LOCAL EXTREMA, INFLECTION POINTS AND INTERVALS OF CONCAVITY
PREREQUISITE KNOWLEDGE:
The student should know how to find the derivative of any given function.
This step by step guide will meet the following objectives:
Objectives:
---------------------------------------
Upon completion of this section, the student should be able to:
• Use derivatives to determine the intervals of increase and decrease of a given function
• Use the First Derivative Test to determine any local maximum or minimum points
• Find inflection points
• Use the concav
11th - 12th, Adult Education, Higher Education
Calculus
Also included in: BASIC CALCULUS
Calculus-Making Observations about the Function and Its Derivatives from Graphs
This discovery activity is made up of 5 part plus a closing question. Part I: Students graph a function and its derivative. From the two graphs students observe that when the graph of the derivative of y1 is positive the graph of y1 is increasing and that when the graph of the derivative of y1 is negative the graph of decreasing. Part II: In part I students studied a function with a minimum. In this part students will repeat the same observations but with a function that has a maximum. Part II
10th - 12th, Higher Education
Calculus, Math
AP Calculus - f' Analysis Cheat Sheet
Help your students organize their thoughts of f' Analysis using thiHelp your students stay organized and master the fundamentals of calculus with this comprehensive, one-page f' Analysis Cheat Sheet. Perfect for AP Calculus students, this resource provides clear and concise explanations of critical points, increasing and decreasing functions, concavity, inflection points, and relative maximums and minimums using both the first and second derivative tests and how to justify them effectively! Key
9th - 12th, Higher Education
Calculus
Curve Sketching Lecture (Differential Calculus 1 Lesson Notes)
This handout is meant as an in-class activity for curve sketching in a differential calculus course. The first few pages contains a review of curve sketching. The curve sketching topics covered are: domainx,y interceptshorizontal asymptotes (using limits)vertical asymptotes (using limits)increasing/decreasing (using first derivative)local max/min (first derivative test)concavity (using the second derivative)inflection pointssketch the graph of the function using all the above informationThe r
12th, Adult Education, Higher Education
Calculus, Math Test Prep
Also included in: BUNDLE: Differential Calculus 1 Lecture Notes / Lessons
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
9th - 12th, Higher Education
Calculus, Graphing
Also included in: Advanced Curve Sketching Practice & Key— Calculus AB/Calculus 1
Applications of Derivatives Cheat Sheet | MVT, EVT, Optimization & Related Rates
Take your students beyond basic derivatives with this powerful Applications of Derivatives Cheat Sheet for AP Calculus! This 2-sided, one-page resource clearly organizes the most important concepts from Units 4 & 5, helping students apply derivatives in real-world and exam-style situations. 📘 What’s Included:• Mean Value Theorem (MVT) • Extreme Value Theorem (EVT) • Critical points and the Candidate’s Test • Increasing & decreasing intervals • First and Second Derivative Tests • Concavity and
9th - 12th, Adult Education, Higher Education
Applied Math, Calculus, Math Test Prep
SIX Curve Sketching Worksheets + Key + Summary of Curve Sketching - Calculus 1
This product (pdf) can be used as an in-class activity / homework / group work for curve sketching in differential calculus. The first 2 pages does a review of curve sketching. There are 6 curve sketching questions, followed by their key. For each question, the student must find the following: - domain - x,y intercepts - horizontal asymptotes (using limits) - vertical asymptotes (using limits) - increasing/decreasing (using first derivative) - local max/min (first derivative test) - concavity
12th, Adult Education, Higher Education
Calculus, Math Test Prep
Graphs of First & Second Derivatives Identify and Match f, f', f''
In this activity students practice identifying the Graphs of a function and its first and second derivative, f, f ', and f ''. They analyze 3 graphs, one blue, one black, and one red, superimposed on the same coordinate grid, to determine which is the graph of original function, the graph of first derivative, and the graph of the second derivative. The activity does not require differentiation, but requires students to understand increasing, decreasing, relative extrema, and concavity. Man
11th - 12th, Higher Education
Calculus, Graphing
Also included in: Calculus Applications of Differentiation Unit Bundle
Calculus 2 Curriculum Bundle
This Calculus 2 Curriculum Bundle includes 58 classroom tested resources which will enhance your lessons and engage your students. My experience has shown that Calculus students succeed with varied lessons and activities and need a curriculum where each day is a new learning experience geared for all types of learners. The resources in this bundle will help you engage all of your students with rigorous and fun activities. Activity-based learning facilitates better understanding and you ca
10th - 12th, Higher Education
Calculus
Calculus BC notes, hw, warm ups and practice quizzes
In this download you will find everything you need to teach all the topics of Calculus BC for the year. Topics stretch from review of prior math to polar functions. PDF and word files are included for all packets. Word files are editable. Each of 10 chapters has notes, homework, warmups and practice quizzes. There are powerpoints of each set of notes to teach with, and they are editable. Filled in notes are included, as well as homework work and answers. The warm ups also have a powerpoint fil
11th - 12th, Higher Education
Calculus, Math, Math Test Prep
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