Question

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

Answer 1

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`

f(x) = `x^3 - x^2 - 8x + 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 .