Find the absolute extrema. f(x)=5-x^{2}\ on\ [-5,4]

Alan Smith

Alan Smith

Answered question

2021-12-09

Find the absolute extrema.
f(x)=5x2 on [5,4]

Answer & Explanation

Paul Mitchell

Paul Mitchell

Beginner2021-12-10Added 40 answers

Given,
f(x)=5x2,[5,4]
Differentiating with respect to x, we get
f'(x)=0-2x
=-2x
Now to find critical numbers, solve the first derivative by equating it to zero. That is,
f'(x)=0
2x=0
x=0
Step 2
Now find the value of the function at critical number and at end points of the given interval.
f(5)=5(5)2
=-20
f(0)=502
=5
f(4)=542
=-11
Hence absolute maximum value is 5 occurs at x=0.
& absolute minimum value is -20 occurs at x=-5.

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