Find the stationary points on the curve y = x^3 + 3x^2 - 9x - 4

A stationary point is where the gradient is exactly zero - the curve is neither increasing or decreasing. This means that we need to differentiate y to find dy/dx and then set this equal to 0. Doing this, using the normal rules for differentiation, we would get 3x^2 + 6x -9 Then, we would set this equal to zero and factorise the equation to find out the x values of our stationary points. Doing this, we get (x + 3)(x - 1) = 0 Leaving x=-3 or x=1 Finally, substitute these values into y = x^3 + 3x^2 -9x -4 and this will give you the y-coordinates to the stationary points. The final answers are therefore (-3,23) and (1,-9)