   Chapter 2.8, Problem 16E

Chapter
Section
Textbook Problem

Make a careful sketch of the graph if .f and below it sketch the graph of f' in the same manner as in Exercises 4-11. Can you guess a formula for f'(x) from its graph?f(x) = sin x

To determine

To sketch: The graph of f(x) and then f(x) below it and guess the formula for f(x).

Explanation

The given function is f(x)=sinx.

Recall the fact that, the derivative of a function at x=a is zero if the function has horizontal tangent at the point x=a.

From the graph, it is observed that the graph has a horizontal tangent at three points. Let the points be A, B, C and D. At these points, the derivative will be zero.

The AB section of the graph has negative slope which implies that the derivative will be negative in the section.

The BC section of the graph has positive slope which implies that the derivative will be positive in the section.

The CD section of the graph has negative slope which implies that the derivative will be negative in the section

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