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 2020-11-02 Answered
Consider the function f(x)=x472x2+9,5x13.
This function has an absolute minimum value =?
and an absolute maximum value =?
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Expert Answer

ottcomn
Answered 2020-11-03 Author has 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

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Jeffrey Jordon
Answered 2021-11-03 Author has 2064 answers

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