Answer:
Minimum at (-2, -16) and maximum at (1, 11).
Step-by-step explanation:
OK. first find the derivative.
y' = 12 - 6x - 6x^2. So for the turning points;
12 - 6X - 6X^2 = 0
-6(x^2 + x - 2)) = 0
-6(x - 1)(x + 2) = 0
x = -2, 1.
These are the values of x at the stationary points on the graph.
To find which is the maxm and which is the minm we evaluate the second derivative:
y" = -6 - 12x
When x = -2 . y" = 18 so this is a minimum.
When x = 1, y" = -18 so this is a maximum.
Substituting the values of x to get the y coordinates:
When x = -2 , y = 4 + 12(-2) - 3(-2)^2 - 2(-2)^3 = -16.
When x = 1 , y = 4 + 12(1) - 3(1)^2 - 2(1)^3 = 11.
