Is #f(x)=(x+3)(x-2)(x-2)# increasing or decreasing at #x=-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 # 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 .
