Question

Find the stationary points of the curve

Answer 1

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.