   Chapter 2.8, Problem 17E

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) = ex

To determine

To sketch: The graph of f(x) and then f(x) below it.

Explanation

The given function is f(x)=ex.

From the graph of f(x), it is clear that the slope is always positive. Thus, the derivative of the graph is always positive.

Draw the tangent to the graph at x=0 and the slope of the graph is computed as follows,

m=0110=11=1

Recall the fact that, the slope of the function at the point x=a is equal to the derivative of the function at that point.

Therefore, f(x)=1 at x=0.

Thus, the graph of the function f(x) passes through the point (0,1)

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