A) at critical points, the derivative of the equation is 0.

First find the derivative

F(X) = 4x3 + 9x2 -12x + 13
F'(x) = 12x2 + 18x - 12

To check whether the values given are critical values, substitute into f'(X). If it is equal to 0, then it is a critical value.


B) To check if it is a maximum or minimum point, use second derivative test and differentiate again

F'(X) = 12x2 + 18x - 12
F''(X) = 24x + 18

Substitute the two values of X given. If the F''(X) is a negative, means it is a maximum. If the F"(X) is positive, then it is a minimum.

Substitute the X values into the original f(X) equation to get their y coordinates. Now, you have the coordinates of the maximum and minimum points for you to sketch the graph.

C) you have the maximum and minimum points. Now you need to find the X intersect and y intersect to sketch the graph.

Give it a try. Hope it helps