Find the absolute maximum and absolute minimum values of f

miyoko23q3

miyoko23q3

Answered question

2021-12-06

Find the absolute maximum and absolute minimum values of f on the given interval.
f(x)=8+54x2x3,[0,4]
absolute minimum value
absolute maximum value

Answer & Explanation

Clara Clark

Clara Clark

Beginner2021-12-07Added 17 answers

Step 1
Given,
f(x)=8+54x2x3 and [0,4].
Step 2
Finding critical point:
f(x)=0
d(8+54x2x3)dx=0
0+542(3x2)=0
6x2=54
x2=9
x=3
x=3,3
Since, -3 doesn't lies in the given interval [0,4].
So, critical point is at x=3.
Step 3
Now, we will find values of function at the point x=0,3 and 4.
f(0)=8+54(0)2(0)3=8
f(3)=8+54(3)2(3)3=116
f(4)=8+54(4)2(4)3=96
Since, f(3)>f(4)>f(0).
The absolute minimum value is 8
and the absolute maximum value is 116

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