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 d2y/dx2 <0 it is a maximum point and if d2y/dx2 >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
y = x3 -27x + c
Find the stationary value of x, let dy/dx=0
Find the value of x at the maximum point, d2y/dx2<0
Find constant (c) by subsitution y=18 and x=-3
Since y = x3 -27x + c
Substitute y=18 and x=-3
Therefore the equation of the curve is y=x3 – 27x – 36
Additional Math (amath) differentiation of gradient to find the y-intercept and equation of curve.