Find the stationary points of the function y = (1/3)x^3 + (1/2)x^2 - 6x + 15

A stationary point is a point on the function where the gradient is zero. The phrase 'stationary point' coming up in a question always indicates that differentiation may be useful to solve it. In this case, the derivative of the function, often expressed as dy/dx, is x^2 + x - 6. As dy/dx is the gradient of the function, set it equal to zero to find stationary points. The easiest way to solve x^2 + x - 6 = 0 is by factorisation. So (x+3)(x-2)=0 gives the solutions x=2 , x=-3. Sub these back in to the original equation to find the corresponding y values. For x=2, y=23/3. For x=-3, y=57/2. The stationary points are therefore at (2, 23/3) and (-3,57/2).