Review question

# What's the area enclosed by $y=x(x-3)^2$ and a tangent? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7386

## Suggestion

Show that the gradient of the curve $y=x(x-3)^2$ is zero at the point $P(1,4)$, and sketch the curve.

When curve sketching, good questions to ask include

• What are the stationary points?

• Where does the curve intercept the axes?

• Are there any asymptotes?

• How does the curve behave for large $x$?

The tangent at $P$ cuts the curve again at $Q$.

What is the equation of the tangent?

How does this help us to find $Q$?

Calculate the area between the chord $PQ$ and the curve.

Can we see on our sketch the area we want to find? What techniques do we have for finding areas?