(a) Explanation The first derivative test for relative extrema consists of following steps: Find all the critical points of a continuous function defined on an interval ( a , b ) . Let’s say ‘c’. If f ( x ) f ( c ) = 0 f ' ' ( c ) = 0 x = c changes sign from positive to ne (b) To determine The second derivative test (c) To determine Which test should be used first.

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ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 4.3, Problem 1PS

(a)

To determine

The first derivative test.

(b)

To determine

The second derivative test

(c)

To determine

Which test should be used first.

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Chapter 4.2, Problem 60PS

Chapter 4.3, Problem 2PS

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Chapter 4 Solutions

Calculus

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The first derivative test.

Solution Summary: The author explains how the first derivative test for relative extrema consists of finding all critical points of a continuous function defined on an interval (a,b,).

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The first derivative test.

The second derivative test

Which test should be used first.

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Chapter 4 Solutions