The function f(x)=-2x^3+30x^2-96x+8 has one local minimum & one local maximum. This function has a local minimum at x equals ______ with value __________ and a local maximum at x equals _______ with value __________ .

Answer 1

f' = -6x^2 + 60x - 96
= -6(x^2-10x+16)
= -6(x-2)(x-8)

So, local min/max occurs where f' = 0

f" = -6(2x-10)
= -12(x-5)

f is max where f" < 0
f is min where f" > 0

Let 'er rip!