Find the absolute maximum and absolute minimum values of the

Lorenzolaji

Lorenzolaji

Answered question

2021-12-04

Find the absolute maximum and absolute minimum values of the function f(x)=x325tan1x, on the interval [0,37]

Answer & Explanation

Coldst

Coldst

Beginner2021-12-05Added 18 answers

Step 1
Maxima minima:
f(x)=x325tan1x at [0,37].
We need to find f'(x)=0
Step 2
f(x)=x325tan1x
f(x)=13251+x2
f(x)=3252x(1+x2)2=650x(1+x2)2>0
So minimum value possible.
f'(x)=0
13251+x2=0
1=3251+x2
1=x2=325
x2=324
x=±18
As the interval is given [0,37].
So Undefined control sequence \cancel.
We take x=37
f(18)=18325tan1(18)
=-474.47
The absolute minimum value is -474.47 at x=18.

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