find the absolute maximum and absolute minimum values of f over the interval. ƒ(x) = (4/x) + ln (x^2), 1<=x <= 4

Brittney Lord 2020-10-26 Answered
find the absolute maximum and absolute minimum values of f over the interval.
ƒ(x)=(4x)+ln(x2),1x4
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Expert Answer

Gennenzip
Answered 2020-10-27 Author has 96 answers
Step 1
Given,
f(x)=(4x)+ln(x2),1x4
Step 2
The absolute maximum or absolute minimum values of a function exist at a point where its first derivative is zero or at the end points of the given interval.
Now differentiating given function with respect to x, we get
f(x)=4x2+1x22x
f(x)=4x2+2x
Now f'(x)=0
4x2+2x=0
4+2x=0
2x=4
x=2
Step 3
Now computing the value of given function at x = 1, x = 4 (end points) and at x = 2 (point at which first derivative is zero).
f(1)=41+ln(12)=4
f(2)=42+ln(22)=3.386294
f(4)=44+ln(42)=3.772588
Step 4
Therefore absolute minimum value is 3.386294 and absolute maximum value is 4.
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Jeffrey Jordon
Answered 2021-11-11 Author has 2047 answers

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