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

1 Answer
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]}