   Chapter 2.8, Problem 48E

Chapter
Section
Textbook Problem

The graphs of a function f and its derivative f' are shown. Which is bigger, f'( –1) or f"(l)? To determine

To Identify: The bigger quantity among f(1) and f(1) with proper explanation.

Explanation

Note:

The derivative is zero where the function has a horizontal tangent.

Graph:

The given graph of f and f is shown in Figure 1.

Observation:

From Figure 1 it is observed that the point where curve c2 has functional value 0 is the same point where graph of curve c1 has horizontal tangent.

By note, c2 is the derivative of the graph curve c1.

Thus, c1=f and c2=f.

Calculation:

From Figure 1, f(1)>0 as the graph of f lies above the x-axis for x=1.

Thus, f(1)>0 (1)

From Figure 1, f(x) has horizontal tangent at x=1.

By note, the value of the derivative of f at x=1 is 0

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