Help with a question.

[Essendon2013]

The curve with the equation ax^3 + x^2 - bx + d has stationary points at x = -1 and x = 3. If it passes through the point (3,11), find the value of a, b and d.

Help with this question would be greatly appreciated

[lzxnl]

so dy/dx=0 at x=-1 and x=3
dydx=3ax^2+2x-b
so 3a-2-b=0
27a+6-b=0
Two equations in two unknowns, just solve.

and when x=3 y=11
27a+9-3b+d=11
so use your values of a and b from above for this