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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2.7, Problem 15E

To determine

**To sketch:** The graph of

Expert Solution

The formula for

The given function is

From the graph of

Draw the tangent to the graph at

Recall the fact that, the slope of the function at the point

Therefore,

Thus, the graph of the function

From the point *A* to left, the slope is increasing slowly. Thus the graph of the function

From the point A to right, the slope increases rapidly. Thus the graph of the function

**Graph:**

Use the online graphing calculator to draw the graph of

**Observation:**

From the Figure 1, it is observed that the graph of the derivative function seems to be a natural exponential function.

Thus, the derivative formula is,