Chapter 2.2, Problem 10E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

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Trace or copy the graph of the given function *f.* (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of

To determine

**To sketch:** The graph of f’ below the graph of the given function using the method of Example 1.

Explanation

**Information used:**

A tangent line is a line that touches the graph but does not intersect it at that point.

The slope of a horizontal tangent line is zero.

**Formula used:**

**Calculation:**

The tangents at x = -2 and x = 1 are horizontal, so the derivative at those points is zero and the graph of derivative crosses the x axis at those points.

Here, f’(-2) = 0 and f’(1) = 0

In given graph, in the interval (-∞, -2) draw tangent at

By using formula,

Thus,

Similarly, in the interval (-2, 1) draw tangent at

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