Find the x coordinates of the stationary points of f(x) = x^3 minus 3x^2 minus 9x plus 5.

1. A stationary point is a point where the gradient of the curve is zero. 2. The derivative gives that gradient, so differentiate first using the rules of differentiation. 3. Differentiating x cubed gives 3x squared, and differentiating minus 3x squared gives minus 6x. 4. Differentiating minus 9x gives minus 9, and the constant 5 differentiates to zero. 5. So the derivative is 3x squared minus 6x minus 9. 6. Set that equal to zero and take out the common factor of 3, giving x squared minus 2x minus 3 equal to zero. 7. That factorises as x minus 3 multiplied by x plus 1, so x equals 3 or x equals minus 1. 8. The pair -3 and 1 is the trap for reversing both signs when reading the factors, x = 3 with x = 1 loses the sign on the second root, and x = 9 comes from squaring 3 instead of solving the factor. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 6: Differential calculus_