Is #f(x)=-4x^3+x^2+2x+2# increasing or decreasing at #x=2#?

decreasing at x = 2

Explanation:

To test if a function is increasing / decreasing at x = a , require to find the value of f'(a).

• If f'(a) > 0 then f(x) is increasing at x = a

• If f'(a) < 0 then f)x) is decreasing at x = a

so f(x) =#- 4x^3 + x^2 + 2x + 2#

hence: f'(x) #= - 12x^2 + 2x + 2#

and# f'(2) = -12(2)^2 +2(2) + 2 = - 42#

since f'(2) < 0 then f(x) is decreasing at x = 2

Here is the graph of f(x)
graph{-4x^3+x^2+2x+2 [-10, 10, -5, 5]}