Find the absolute maximum and absolute minimum values of f on the given interval. f(x)=4x^3-6x^2-24x+9,[-2,3] absolute minimum value-? absolute maximum value-?

Anonym 2020-12-24 Answered
Find the absolute maximum and absolute minimum values of f on the given interval.
f(x)=4x36x224x+9,[2,3]
absolute minimum value-?
absolute maximum value-?
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Expert Answer

dessinemoie
Answered 2020-12-25 Author has 90 answers
Step 1
We will find the first derivative using the power rule
f(x)=4x36x224x+9
f(x)=4(3x2)6(2x)24
f(x)=12x212x24
Step 2
We find the critical values by solving f'(x)=0
12x212x24=0
12(x2x2)=0
12(x-2)(x+1)=0
x=2,-1
Then we find the values of the function at the critical points and at the endpoints.
f(x)=4x36x224x+9
f(2)=4(2)36(2)224(2)+9=1
f(1)=4(1)36(1)224(1)+9=23 (max)
f(2)=4(2)36(2)224(2)+9=31 (min)
f(3)=4(3)36(3)224(3)+9=9
Result:
Absolute minimum value= -31
Absolute maximum value=23
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Jeffrey Jordon
Answered 2021-11-11 Author has 2047 answers

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