Find if f(x)=3x^{4}-4x^{3} has any absolute extreme value/values in (-2,

Cheexorgeny 2021-12-09 Answered
Find if f(x)=3x44x3 has any absolute extreme value/values in (2,+).
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Expert Answer

yotaniwc
Answered 2021-12-10 Author has 34 answers
Step 1
Given
f(x)=3x44x3
To find
Absolute maximum and absolute minimum values.
Step 2
f(x)=3x44x3
f(x)=12x312x2
f'(x)=0
12x312x2=0
12x2(x1)=0
x2=0,(x1)=0
x=0,0,1
Critical points=0,1
f(0)=0 , f(1)=-1.
f(2)=3(2)44(2)3=3×16+4(8)=48+32=80.
The absolute maximum value is 80 at -2 and minimum value is -1 at 1.
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