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# Answer: What is the First Derivative Test for Local

ISBN: 9780321884077 57

## Solution for problem 8QGY Chapter 4

Thomas' Calculus: Early Transcendentals | 13th Edition

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Problem 8QGY

What is the First Derivative Test for Local Extreme Values? Give examples of how it is applied.

Step-by-Step Solution:

Step 1 of 3:

In this problem, we need to explain the First Derivative test for Local Extreme values with an example.

Step 2 of 3:

The First Derivative Test for Local Extreme Values:

First Derivative Test for Local Extrema is defined as if f has a local maximum or minimum value at interior point c of its domain then

If  changes sign from negative to positive at c, then f has a local minimum at c.If  changes sign from positive to negative at c, then f has a local maximum at c.

Now we discuss local maximum and local minimum.

Local Maximum:

According to the definition of The First Derivative Test for the Local Extreme value, a function f has a local maximum value at a point c within its domain D if  for all  lying in some open interval containing c.

Local Minimum:

According to the definition of The First Derivative Test for the Local Extreme value, a function f has a local minimum value at a point c within its domain D if  for all  lying in some open interval containing c.

Now we see by the graph:

Step 3 of 3

##### ISBN: 9780321884077

Since the solution to 8QGY from 4 chapter was answered, more than 228 students have viewed the full step-by-step answer. This full solution covers the following key subjects: applied, derivative, Examples, Extreme, give. This expansive textbook survival guide covers 138 chapters, and 9198 solutions. The answer to “What is the First Derivative Test for Local Extreme Values? Give examples of how it is applied.” is broken down into a number of easy to follow steps, and 17 words. The full step-by-step solution to problem: 8QGY from chapter: 4 was answered by , our top Calculus solution expert on 08/01/17, 02:37PM. This textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13. Thomas' Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321884077.

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Answer: What is the First Derivative Test for Local

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