Is f(x)=(x+3)(x-2)(x-2)f(x)=(x+3)(x2)(x2) increasing or decreasing at x=-2x=2?

1 Answer
Jan 17, 2016

increasing at x = - 2

Explanation:

first expand the brackets of the function (using FOIL) then differentiate f(x) and check it's value.

(x + 3 )(x^2 - 4x + 4 ) = x^3 - 2x^2 - 8x x24x+4)=x32x28x

f(x) = x^3 - x^2 - 8x + 12x3x28x+12

rArr f'(x) = 3x^2 - 2x - 8

f'(-2) = 3(-2)^2 -2(-2) -8 = 12 + 4 - 8 = 8 > 0

since f'(-2) > 0 then f(x) is increasing at x = -2 .