f(x) = 1 + 3x² –- 2.x³ Find the local maximum and minimum values of f using both the First and Second Derivative Tests.

Calculus: Early Transcendentals
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Author:James Stewart
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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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21:05
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ex10
2. 计算题
= 1 + 3x? - 2x3
Find the local maximum and minimum values of f using
both the First and Second Derivative Tests.
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Transcribed Image Text:21:05 .... ex10 2. 计算题 = 1 + 3x? - 2x3 Find the local maximum and minimum values of f using both the First and Second Derivative Tests. 输入答案 2/2 <上一题 提交 答题卡
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Step 1

To Determine: find the local maximum and minimum values of f using both first derivative and second derivative test

Given: we have a function f(x)=1+3x2-2x3

Explanation:  we have a function f(x)=1+3x2-2x3

A) first and second derivative test: if we have a function f(x) then local maximum and minimum is given by 

for local maximum value f ''(x)<0 at critical points.

for local minimum value f ''(x)>0 at critical points.

                                  f'(x)=6x-6x2

now to find the critical point put f'(x)=0 then we have 

                                 6x-6x2=06x(1-x)=0x=0, x=1

now the second derivative will be 

                            f ''(x)=6-12x

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