Calculus Question

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Step 1

Given :

Function, derivative of function and second derivative.

Calculus homework question answer, step 1, image 1

Step 2

Part(a)

The function is increasing when Calculus homework question answer, step 2, image 1 where Calculus homework question answer, step 2, image 2and Calculus homework question answer, step 2, image 3.

First find the critical point by equating zero with derivative of function. and the find the interval and find where the function is increasing and where the function is decreasing.

Calculus homework question answer, step 2, image 4

The critical point is 6 and 8.

now find the interval.

Calculus homework question answer, step 2, image 5

Step 3

To find the increasing or decreasing find the nature of sign in that interval.

  Calculus homework question answer, step 3, image 1 Calculus homework question answer, step 3, image 2 Calculus homework question answer, step 3, image 3
Sign + - -
Behavior Increasing decreasing decreasing

Therefore the function is increasing in the interval Calculus homework question answer, step 3, image 4.

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