a. Explanation The given function is f ( x ) = 1 3 x 3 − x 2 + x − 6 . Find the critical points to find the increasing and decreasing intervals. To find the critical points, set the first derivative to 0. f ( x ) = 1 3 x 3 − x 2 + x − 6 f ′ ( x ) = x 2 − 2 x + 1 = ( x − 1 ) 2 Set ( x − 1 ) 2 = 0 and solve for x . ( x − 1 ) 2 = 0 x − 1 = 0 x = 1 Therefore, the critical point divides the real line into two parts such as ( − ∞ , 1 ) ∪ ( 1 , ∞ ) b. To determine The relative extrema of the function f ( x ) = 1 3 x 3 − x 2 + x − 6 . c. To determine The intervals on which the graph of the function f ( x ) = 1 3 x 3 − x 2 + x − 6 concave upward and concave downward. d. To determine The inflection point of the function f ( x ) = 1 3 x 3 − x 2 + x − 6 .

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

10th Edition

ISBN: 9780357465400

Author: Tan

Publisher: CENGAGE L

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In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 4, Problem 1RE

To determine

The intervals on which the function f(x)=13x3−x2+x−6 is increasing and decreasing.

To determine

The relative extrema of the function f(x)=13x3−x2+x−6.

To determine

The intervals on which the graph of the function f(x)=13x3−x2+x−6 concave upward and concave downward.

To determine

The inflection point of the function f(x)=13x3−x2+x−6.

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Chapter 4, Problem 10CRQ

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Chapter 4 Solutions

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

Ch. 4.1 - Explain each of the following: a. f is increasing...Ch. 4.1 - Prob. 2CQ Ch. 4.1 - Prob. 3CQ Ch. 4.1 - Prob. 4CQ Ch. 4.1 - Prob. 5CQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E

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The intervals on which the function f ( x ) = 1 3 x 3 − x 2 + x − 6 is increasing and decreasing.

Solution Summary: The author explains the intervals on which the function f(x) is increasing and decreasing. The critical points divide the real line into two parts.

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The intervals on which the function f(x)=13x3−x2+x−6 is increasing and decreasing.

The relative extrema of the function f(x)=13x3−x2+x−6.

The intervals on which the graph of the function f(x)=13x3−x2+x−6 concave upward and concave downward.

The inflection point of the function f(x)=13x3−x2+x−6.

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Chapter 4 Solutions