How do you find the extremas for #f(x)=x^3 - 9x^2 + 27x#?

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Answer 1 · 2015-04-27T17:41:32

#f(x) = x^3 -9x^2 +27x#.

Find the critical number(s):

#f'(x) = 3x^2 - 18x +27#

#f'(x)# never fails to exists.

#f'(x) = 0# when

#3(x^2-6x+9)=0#

#3(x-3)^2 = 0#

At #x=3#.

The only critical number is #3#

Test the critical number:

#f'(x)# is positive on both side of #f(3)# is neither a local maximum nor a local minimum. There are no other candidates, so there are no extrema.