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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
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) = In x

To determine

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

Explanation

The given function is f(x)=lnx.

From the graph of f(x)=lnx, 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=1 and the slope of the graph at x=1 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=1.

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

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