   Chapter 2.8, Problem 47E

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

Graph:

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

Observation:

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

Thus, c1=f and c2=f.

Calculation:

From the Figure 1, it is observed that f(1)<0 as the graph of f lies below the x-axis for x=1.

Thus, f(1)<0. (1)

From the Figure 1, it is observed that f(x) has a horizontal tangent at x=1.

Recall that the derivative of a function is zero where the function has a horizontal tangent.

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

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