Asked by Callie

Find the local maximum and local minimum of the function. f(x) = x^3 − 12x^2 − 27x + 7
Answered by Reiny
dy/dx = 3x^2 - 24x - 27
= 0 for a max/min

divide by 3
x^2 - 8x - 9 = 0
it factors nicely ...
(x-9)(x+1) = 0
x = 9 or x = -1

f(9) = .....
f(-1) = ....

take over.

this confirms our work
http://www.wolframalpha.com/input/?i=plot+f%28x%29+%3D+x%5E3+%E2%88%92+12x%5E2+%E2%88%92+27x+%2B+7
Answered by Callie
Those are the answers I got that I thought were wrong, but the online assignment wanted the value of f(9)=-479 and f(-1)=21, not 9 and -1. Thank you!
Answered by Reiny
exactly.

I left it up to you to finish the problem.
Oh well ....

f(9) = 9^3 - 12(9)^2 - 27(9) + 7
= -479

etc for f(-1) = 21
Answered by Reiny
btw, I also did your other very long question.
Did you look at it ?
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