Review question

# Can we sketch the graph of $y=x(x+1)(x-2)^4$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8387

## Question

The curve $C$ has equation $y=x(x+1)(x-2)^4.$ Show that the gradient of $C$ is $(x-2)^3(6x^2+x-2)$ and find the coordinates of all the stationary points. Determine the nature of each stationary point and sketch $C$.

In separate diagrams draw sketches of the curves whose equations are:

1. $y^2=x(x+1)(x-2)^4$;

2. $y=x^2(x^2+1)(x^2-2)^4$.

In each case, you should pay particular attention to the points where the curve meets the $x$ axis.