Find the absolute maximum and absolute minimum values of f on the given interval. f(x)=x+4/x, [0.2,8] absolute minimum value-? absolute maximum value-?

Cem Hayes 2020-11-12 Answered
Find the absolute maximum and absolute minimum values of f on the given interval.
f(x)=x+4x,[0.2,8]
absolute minimum value-?
absolute maximum value-?
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Expert Answer

Bertha Stark
Answered 2020-11-13 Author has 96 answers
Step 1
We have given
f(x)=x+4x,[0.2,8]
Step 2
Obtain the critical values
f(x)=14x2
Then
f'(x)=0
14x2=0
x24x2=0
(x+2)(x2)x2=0
x=2,2
Step 3
Since -2 does not lie in the given interval, x = 2 is the only critical number.
Evaluate f(x) at the endpoints and the critical point.
f(0.2)=0.2+40.2=20.2
f(2)=2+42=4
f(8)=8+48=8.5
Step 4
Therefore, the function has
absolute minimum value 4
absolute maximum value 20.2
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