if: f(x) = x3 - 4xe-2x Then: f'(x) = 3x2 - [ 4e-2x + 2(4x / -2x) ] = 3x2 - 4e-2x + 4
if f(x) = x3 + 4x2 - 11x - 30, then yes, (x - 3) is indeed a factor. f(x) = x3 + 4x2 - 11x - 30 ∴ f(x) = (x - 3)(x2 + 7x + 10) ∴ f(x) = (x - 3)(x + 2)(x + 5)