Question

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

Answer 1

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]}