Find the absolute maximum and minimum values of f on

Grady Turner

Grady Turner

Answered question

2021-12-07

Find the absolute maximum and minimum values of f on the given closed interval, and state where those values occur
f(x)=(x2)3;[1,4]

Answer & Explanation

Lupe Kirkland

Lupe Kirkland

Beginner2021-12-08Added 21 answers

Step 1
To Determine:
Find the absolute maximum and minimum values of f on the given closed interval [1, 4], and state where those values occur
f(x)=(x2)3
Step 2
Explanation:
In order to find the absolute maximum and minimum values, we will find the critical values to find the first derivative of the given function.
f(x)=3(x2)2
Now put f'(x)=0 to find the critical points
3(x2)2=0
(x2)2=0
x-2=0
x=2
Evaluate f(x) at all the critical values and also at the interval two values 1 and 4
f(1)=(12)3=1
f(2)=(22)3=0
f(4)=(42)3=8
The absolute maximum of f(x) on [1, 4] will be the largest number found in previous step ,while the absolute minimum of f(x) on [1, 4]
Absolute maximum = 8
Absolute minimum = -1
Step 3
Answer:
Absolute maximum = 8
Absolute minimum = -1

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?