The point (2, −8) is on the curve y = x³ − px + q.

a. Use this information to find a relationship between p and q.

b. Find the gradient function dy/dx.

The tangent to this curve at the point (2, −8) is parallel to the x-axis.

c. Use this information to find the value of p.

d. Find the coordinates of the other point where the tangent is parallel to the x-axis.

e. State the coordinates of the point P where the curve crosses the y-axis.

f. Find the equation of the normal to the curve at the point P.