Find the absolute maximum and absolute minimum values of f

zachutnat4o

zachutnat4o

Answered question

2021-12-04

Find the absolute maximum and absolute minimum values of f on the given interval.
f(x)=4x232x+2,[0,9]
absolute minimum value
absolute maximum value

Answer & Explanation

Thomas Conway

Thomas Conway

Beginner2021-12-05Added 10 answers

Step 1
The given function is:
f(x)=4x232x+2...(1)
Differentiate the above function with respect to x.
f'(x)=8x-32
Substitute f'(x)=0
8x-32=0
The critical point is given as:
8x-32=0
x=328
=4
The absolute maximum and absolute minimum on the interval [0,9] is given as:
f(4)=4(4)232(4)+2
=64-128+2
=-62
f(0)=4(0)-32(0)+2
=2
f(9)=4(9)232(9)+2
=324-288+2
=38
The absolute maximum is 38 at x=9
The absolute minimum is -62 at x=4
Step 2
Therefore, the given function has absolute maximum as 38 at x=9 and absolute minimum as -62 at x=4 on the given interval [0,9]

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?