What are the local extrema, if any, of f(x)= –2x^3 + 6x^2 + 18x –18?

1 Answer
Mar 22, 2016

Maximum f is f(5/2) = 69.25. Minimum f is f(-3/2) = 11.25.

Explanation:

d/dx(f(x))=-6x^2+12x+18 = 0, when x =5/2 and -3/2

The second derivative is -12x+12=12(1-x) < 0 at x = 5/2 and > 0 at x = 3/2.
So, f(5/2) is the local (for finite x) maximum and f(-3/2) is the local (for finite x) minimum.

As xto oo, fto -oo and as xto-oo, fto+oo..