Find the x-values of the turning points on the graph, y=(3-x)(x^2-2)

The minimum point occurs where dy/dx=0

We have 2 options: 1.) Expanding the brackets 2.) The product rule of differentiation

The shortest is the product rule: dy/dx= (d/dx)(3-x).(x²-2) + (3-x).(d/dx)(x²-2)

dy/dx=(-1).(x²-2) + (3-x).(2x)

dy/dx= -x²+2 +6x-2x²

dy/dx=-3x²+6x+2

-3x²+6x+2=0 gives x=1-root(5/3), and, x=1+root(5/3)