   Chapter 4.1, Problem 52E

Chapter
Section
Textbook Problem

HOW DO YOU SEE IT? Use the graph of f’ shown in the figure to answer the following. (a) Approximate the slope of f at x = 4 . Explain.(b) Is f ( 5 ) − f ( 4 ) > 0 ? Explain.(c) Approximate the value of x where f is maximum Explain.(d) Approximate any open intervals on which the graph of f is concave upward and any open intervals on which it is concave downward. Approximate the coordinates of any points of inflection.

(a)

To determine
The approximate slope of function f at x=4 from the graph as shown below.

Explanation

Given:

The graph of the function f,

Please Refer the figure in the given question.

Explanation:

Since, f(x) is the slope of the function f(x)

(b)

To determine
Whether f(5)f(4)>0 from the graph as shown below.

(c)

To determine
The approximate value of x where f is maximum from the graph as shown below.

(d)

To determine
Any open intervals on which the graph of f is concave upward and any open intervals on which it is concave downward from the graph as shown below. Also, approximate the x-coordinates of any points of inflection.

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