   Chapter 2.2, Problem 10E

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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 f ′ below it. 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:

slope =  y2-y1x2-x1

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 x = -2.5. The tangent passing through the points (-2.6, 2) and (-2.3, 1.4).

By using formula,

slope =  1.4-2-2.3+2.6= -2

Thus,

f-2.5= -2

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

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