Consider the function f(x)=x^{4}−72x^{2}+9, -5\leq x\leq 13. This function has an absolute minimum value =? and an absolute maximum value =?

Aneeka Hunt

Aneeka Hunt

Answered question

2020-11-02

Consider the function f(x)=x472x2+9,5x13.
This function has an absolute minimum value =?
and an absolute maximum value =?

Answer & Explanation

ottcomn

ottcomn

Skilled2020-11-03Added 97 answers

f(x)=x472x2+9
fprime(x)=4x372(2x)+0
fprime(x)=4x3144x
For the critical numbers fprime(x)=0
4x3144x=0
4x(x236)=0
4x(x+6)(x6)=0
x=0,6,6
Note: x=6 is not in the interval 5x13
Step 2
Now we find the value of f(x) at the end points and at the critical points
f(x)=x472x2+9
f(5)=1166
f(0)=9
f(6)=1287(min)
f(13)=16402(max)
Answer:
This function has an absolute minimum value = -1287
and an absolute maximum value =16402

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-03Added 2605 answers

Answer is given below (on video)

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?