Any point on a curve that has stationary point (maximum/minimum) the gradient is equal to zero (dy/dx =0).

To determine if that particular point is maximum or minimum, do a second order differentiation d2y/dx2 , if d^{2}y/dx^{2} <0 it is a maximum point and if d^{2}y/dx^{2} >0 it is a minimum point.

Integrate the expression dy/dx to find the equation of the curve , don’t forget to find the value of the constant (c) substitution the coordinates of the maximum point into the equation

Integrate

y = x^{3 }-27x + c

Find the stationary value of x, let dy/dx=0

Find the value of x at the maximum point, d^{2}y/dx^{2}<0

Find constant (c) by subsitution y=18 and x=-3

Since y = x^{3 }-27x + c

Substitute y=18 and x=-3

18=(-3)-27(-3)+c

c=-36

Therefore the equation of the curve is y=x^{3} – 27x – 36

Additional Math (amath) differentiation of gradient to find the y-intercept and equation of curve.