Find the absolute minimum and absolute maximum values of f

gabioskay7

gabioskay7

Answered question

2021-12-03

Find the absolute minimum and absolute maximum values of f on the given interval.
f(x)=xln(7x), [12,2]
absolute minimum B
absolute maximum B

Answer & Explanation

George Spencer

George Spencer

Beginner2021-12-04Added 12 answers

Step 1
Consider the provided function,
f(x)=xln(7x), [12,2]
Find the absolute minimum and maximum values of f on the given interval.
First find the derivative of the function,
ddx[f(x)]=ddx[xln(7x)]
f(x)=117x7
=11x
Step 2
Now, find the critical point.
f'(x)=0
So,
11x=0
x-1=0
x=1
So, find the value of the function.
x=12,1,2
Step 3
Find the value of the function at x=12.
f(12)=12ln(72)
=0.5[ln(7)ln(2)]
=0.5-1.25276
=-0.75276
And at x=1,
f(1)=1ln(7)
=1-1.94591
=-0.94591
Step 4
And x=2,
f(2)=2ln(14)
=2-2.63905
=-0.63905
Therefore, we can see that the absolute maximum and minimum values is shown below,
-0.63905 and -0.94591.
Hence.

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