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)
ZE
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