Find the derivative of the function f (x) = 2x³-3x² + 6 and the values of f` (-2) and f` (2)

First, let’s calculate the derivative of the given function:

f ′ (x) = (2x ^ 3 – 3x ^ 2 + 6) ′ = (2x ^ 3) ′ + (-3x ^ 2) ′ + 6 ′ =

= 2 * 3 * x ^ (3 – 1) – 3 * 2 * x ^ (2 – 1) + 0 = 6x ^ 2 – 6x = 6x * (x – 1).

Now we find the values of the derivative at x = -2 and x = 2:

f ′ (- 2) = 6 * (-2) * (-2 – 1) = -12 * (-3) = 36;

f ′ (2) = 6 * 2 * (2 – 1) = 12 * 1 = 12.

Answer: f ′ (x) = 6x * (x – 1); f ′ (- 2) = 36; f ′ (2) = 12.