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Derivatives Teacher Resources
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This is comprehensive lesson that considers many aspects of quadratic functions. It includes using factoring, completing the square and the use of the quadratic formula for finding the zeros of the function (including imaginary roots). It also reverses the whole process by looking at either different graphs of quadratic functions or zeros that are given and challenges the learner to derive the function. This lesson provides an excellent review for the second year algebra student or a multi-lesson unit for the more novice student.
Use real world scenarios to facilitate discussion of the relationship between variables and how they are represented graphically and analytically. This can work in part as an introduction to functions, as a complete lesson, or as an extension to a unit on the library of functions.
Learners are given a graph of a parabola on a coordinate system, but intercepts and vertex are not labeled. The task is to analyze eight given quadratic functions and determine which ones might possibly be represented by the graph. The focus of the exercise is on determining key features of a graph, such as intercepts, maximum or minimum, and which way the graph opens, from the equation. The activity is best suited for use in Algebra I after studying the different forms of a quadratic equation, or as a review exercise in Algebra II.
In this derivative functions learning exercise, students solve and complete 17 various types of problems. First, they find the slope of the tangent line at a given point. Then, students find the derivative of the given functions. In addition, they find the value of the derivative of the given function at the indicate point.
Use an activity to illustrate the different forms of a quadratic function. Here, the task asks learners to use composition of given functions to build an explicit function. The process emphasizes the impact of the order of composition and the effect that each composition has on the graph of the function. The problem assumes that students are familiar with the process of completing the square.
This activity guides learners through an exploration of common transformations of the graph of a function. Given the graph of a function f(x), students generate the graphs of f(x + c), f(x) + c, and cf(x) for specific values of c. The focus is more abstract than algebraic because no formula for the function is given. The task can be used either for instruction or assessment.
Students explore the concept of cubic functions. In this cubic functions lesson, students graph cubic functions on their calculator. Students determine the local maximum and minimum points and the tangent line from the x-intercept to a point on the cubic function. Students graph various shifts in the cubic function and describe its' max. and min. points.
High schoolers graph exponential equations and solve application problems using exponential functions. They re-enact a story about a peasant worker whose payment for services is rice grains doubled on a checker board. They place M & Ms on a checkerboard and mark the number on a graph. They double the number for each space on the board and create a graph of the data.
Learners follow detailed directions to illustrate Rolle's Theorem on their graphing calculator. In this application of derivatives worksheet, students input a given function into their graphing calculator and graph it. They then calculate and graph the derivative of the original function.
A detailed lesson plan that uses a Ferris wheel to study the equations and graphs of trigonometric functions. Learners must match trigonometric graphs (in the form h = a + b cos ct) to their equations and also create their own equation to describe the movement of the Ferris wheel. Includes a pre-assessment, group activity, and answer key with many helpful tips to facilitate the lesson. Also includes a corresponding PowerPoint.
In this differentiating special functions worksheet, students solve and complete 5 various types of problems. First, they differentiate each of the given functions. Then, students complete the table using a calculator and plot the points on a graph. In addition they find the slope of the function at a given point.