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How do my students learn the significance of taking the second derivative? This introduction to determining concavity, inflection points, and using the second derivative test is easy to follow and understand. The anchor charts lead the students into determining concavity and locating inflection points. Using the second derivative test, they will also practice determining if critical numbers are relative extrema. Included in this product:· Lesson on the Second Derivative with examples. · Guide

Students often find success with the first derivative test once they understand how to apply it. By working through the examples visually and analytically, then applying the anchor chart, students can determine where the relative extrema are located. This lesson can be used as an introduction to the first derivative test, as remediation, or as review. Concepts included in this lesson are:Determining increasing and decreasing intervals. The First Derivative Test.Relative maximum and minimum

Students often feel overwhelmed when learning about theorems. This introductory lesson offers a concise explanation to the conditions and conclusion for the Mean Value Theorem. By following the included anchor chart, students determine when and how to apply the Mean Value Theorem. Concepts included in this lesson are:Slope of a secant line.Slope of a tangent line. Conditions for the Mean Value Theorem.The Mean Value Theorem.Applying the Mean Value Theorem.Determining the value for c. You ca

Extrema, maximums and minimums, are used for many applications in calculus. Graphing and optimization will be the primary uses in this course. In this lesson students will explore extrema graphically and numerically. Concepts included in this lesson are:· Identifying maximums and minimums graphically. · Determining critical numbers. · Identifying the difference between absolute and local or relative extrema. · Comparing endpoints and critical numbers to determine absolute maximums and mini

AP Calculus AB and BC Course and Exam Description, Effective Fall 2019 What is the difference between total and displaced distances? The vocabulary may be new, but students have been finding displaced distance for many years. Now, they will determine total distance by applying concepts when deriving velocity from position. Concepts included in this lesson are:· Velocity is the derivative of position/distance. · Determining zero velocity. · Positive and negative velocity. · Change

Students love learning L’Hospital’s rule because it makes limits so much easier. Concepts included in this lesson are:· Identifying indeterminate forms. · Applying L’Hospital’s rule. · When L’Hospital’s rule does not apply. · Using L’Hospital’s rule more than once. The no prep lesson and worksheet are easy for students to follow and complete. You can print this lesson and use it as an in-class activity or download the digital learning choice for distance learning students. Even if you have

Estimating is a common skill in all math classes. Linear approximations are the primary type of estimation calculus students learn. Students will gain a solid understanding of this skill which is the basis for future advanced calculus concepts such as Newton’s Method. Concepts included in this lesson are:· Review of tangent lines. · Linear approximations. · Determining if the approximation is an overestimation or an underestimation. · Optional linear approximation for trigonometric function

In this second lesson on related rates, students will further study classic uses of this concept from falling ladders to rates of change in elevation. Related rates included in this lesson are:· A falling ladder. · Objects moving apart at right angles. · Change in the angle of elevation. · Change in size of similar triangles. The no prep lesson and worksheet are easy for students to follow and complete. You can print this lesson and use it as an in-class activity or download the digital lea

In this first lesson on related rates, students will learn how to compute change in measurements such as the change in the height of a cone given its dimensions and its change in volume. Concepts included in this lesson are:· What is a related rate. · Related rates of common objects such as circles, cubes and spheres. · Related rates where a ratio relating two measurements is substituted into a formula. (i.e. substituting base for height in determining the area of a triangle given a ratio betw

The no prep lesson and worksheet are easy for students to follow and complete. Students will learn step-by-step how to find velocity and acceleration at a point, and then determine if an object is speeding up or slowing down. You can print this lesson and use it as an in-class activity or download the digital learning choice for distance learning students. Even if you have a hybrid class, both types of students can access this lesson. Also, this can be used for students who were absent when the

The third unit in AP Calculus is “Differentiation: Composite, Implicit, and Inverse Functions.” These lessons offer students a basic understanding of the Chain Rule, Implicit Differentiation, Inverse Functions, Inverse Trig Functions, and Higher Order Derivatives. Also, students will practice solving several types of questions that have been asked on previous AP exams. Students are exposed to derivations of many of the derivatives such as arctanx, but the emphasis is on practice in problem solvi

Many students have difficulty relating the inverse trig functions with their derivatives. By using a right triangle to derive some of the inverse derivatives, students can better understand these formulas. Then the students will use the inverse derivatives in the guided practice and formative assessment. The first page of the worksheet is determining derivatives containing inverse trig. The second page is determining the equation of a tangent line and finally deriving the derivative of the inver

If you can take a derivative once, can you take it again? Yes, you can! In this lesson, students will practice determining the second derivative of functions. Several additional concepts have been questions on previous AP exams, such as identifying derivatives of a polynomial function on a graph, and students will have an opportunity to explore these. Concepts included in this lesson are:· Second derivatives · Inductive reasoning to determine patterns in higher order derivatives. · Identifyin

Students should review inverse functions before they learn to take their derivatives. In this lesson students review what an inverse function is. Then using the Chain Rule, we derive the derivative of an inverse function and practice determining the inverse at a point. Although determining the derivative of an inverse function is not a heavily tested concept, an understanding of inverses and their derivatives is a foundational concept. Concepts included in this lesson are:· Review of inverse

Determining a derivative implicitly is a necessary skill for many problems in calculus. In fact, students will find related rates much easier if they have a solid understanding of implicit differentiation. This lesson will compare explicit and implicit differentiation. In addition to determining a derivative implicitly, students will review determining the equation of a tangent line. Concepts included in this lesson are:· Explicit differentiation. · Implicit differentiation. · Determining the

How do I explain the Chain Rule to my students? Many students struggle with “seeing” the composition of a function, which makes applying the Chain Rule difficult. In this lesson, students will review composite functions and then learn how to apply the Chain Rule, both in a formal way and a more relatable way. Several examples are given, and then students have guided practice problems before they complete the worksheet, which can be used as a formative assessment. This lesson covers the Chain Rul

The Second Unit in AP Calculus is “Differentiation: Definition and Fundamental Properties”. This bundle of ten lessons covers all the standards in this calculus unit. Students will gain a basic understanding of all the concepts from the definition of a derivatives to rules for trigonometry, powers, and products and quotients. Plus, each lesson offers a worksheet which may be used as a formative assessment. Lessons covered in this bundle are:· What is a Derivative · Definition of a Derivative

Do your students have a hard time remembering the Product and the Quotient Rules? The two lessons included in this bundle teach the rules, offer a lot of practice, and compare the rules to make them easier to learn and remember. Concepts in these lessons include:· The Product Rule and the Quotient Rule. · How to apply the rules. · Evaluating problems using the Product and Quotient Rules. · Derivations of the both the Product Rule and the Quotient Rules. (Optional) You can print these no pr

Are there derivatives for the other trig functions? Yes, there are, and we can even derive them easily. In this lesson students will learn the derivatives of all the trig functions and practice how to apply them. Concepts in this lesson are:· Derivations of other trig functions using Quotient Rule with sinx and cosx. · Determining derivatives. · Evaluating derivatives. · Comprehensive chart of all derivatives. (Chain rule not yet included.) You can print this no prep lesson and use it as

Are your students overwhelmed with the Quotient Rule? The Quotient Rule is a long formula, but when we compare it to the Product Rule and then practice using it, the Quotient Rule will be much less intimidating . Concepts in this lesson are:· The Quotient Rule. · Comparison of Product Rule and Quotient Rule · Applying the Quotient Rule. (Anchor Chart included.) · Derivation of the Quotient Rule. (Optional) You can print this no prep lesson and use it as an in-class activity or download the