The function y = | sin x | by the help of transformation.

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Explain the key points and reasons for 12.8.2 (1) and 12.8.2 (2)

Answer 1

Question

Chapter D, Problem 81E

To determine

To sketch: The function y=|sinx| by the help of transformation.

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Explain the key points and reasons for 12.8.2 (1) and 12.8.2 (2)

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Consider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?