Find the absolute maximum value and the absolute minimum value,

Sherry Becker

Sherry Becker

Answered question

2021-12-06

Find the absolute maximum value and the absolute minimum value, if any, of the function.
g(x)=x3+3x21 on [-3,1]

Answer & Explanation

Susan Yang

Susan Yang

Beginner2021-12-07Added 20 answers

Step 1
Given
g(x)=x3+3x21
first differentiate given function g,
g(x)=3x2+6x
To find the critical point equate the derivative to zero
g'(x)=0
3x2+6x=0
3x(x+2)=0
x=0 or x+2=0
x+2=0
x=-2
when x=0
g(0)=03+3×021
=-1
when x=-2
g(2)=(2)3+3(2)21
=-8+12-1
=3
Hence the critical points are (0,-1) and (-2,3)
Step 2
The given interval is [-3,1]
g(3)=(3)3+3(3)21
=-27+27-1
=-1
g(1)=(1)3+3(1)21
=1+3-1
=3
Here
The absolute minimum is at (-3,-1) and (0,-1)
The absolute maximum is at (-2,3) and (1,3)

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