What are the extrema of #f(x) = x^3 - 27x#?

1 Answer
Trevor Ryan.
Nov 1, 2015

#(-3, 54) and (3, -54)#

Explanation:

Relative maximum and minimum points occur when the derivative is zero, that is when #f'(x)=0#.
So in this case, when #3x^2-27=0#
#=>x=+-3.

Since the second derivative #f''(-3)<0 and f''(3)>0#, it implies that a relative maximum occurs at x=-3 and a relative minimum at x=3.

But: #f(-3)=54 and f(3)=-54# which implies that #(-3, 54)# is a relative maximum and #(3, -54)# is a relative minimum.

graph{x^3-27x [-115.9, 121.4, -58.1, 60.5]}

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