   Chapter 3.3, Problem 2E

Chapter
Section
Textbook Problem

# 1-2 Use the given graph of f to find the following.(a) The open intervals on which f is increasing.(b) The open intervals on which f is decreasing.(c) The open intervals on which f is concave upward.(d) The open intervals on which f is concave downward.(e) The coordinates of the points of inflection. To determine

(a)

To find:

The open interval on which f  is increasing.

Explanation

1) Concept:

From the graph, find the interval in which f(x) is increasing.

2) Calculation:

From the graph, the values of f(x) are increasing when x is increasing from 0 to 1 and 3to 7.

Therefore f(x)  is increasing in the intervals (0, 1

To determine

(b)

To find:

The open interval on which f  is decreasing.

To determine

(c)

To find:

The open intervals on which f is concave upward.

To determine

(d)

To find:

The open intervals on which f is concave downward.

To determine

(e)

To find:

Coordinates of points of inflection.

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