Review question

# If $dy/dx$ is inversely proportional to $x^2$, can we find $y$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7410

## Suggestion

1. Show that the curve $y=x(5-x)^4$ has a turning point where $x=5$. Determine whether this turning point is a maximum or a minimum.

How can we find the turning points of a function?

What methods do we know for determining the nature of a turning point?

Which method works best in this case?

1. It is given that that $\dfrac{dy}{dx}$ is inversely proportional to $x^2$ and that $y$ and $\dfrac{dy}{dx}$ are each equal to $1$ when $x=2$. Express $y$ in terms of $x$.

What does it mean for $a$ to be inversely proportional to $b$? Can you write this mathematically?

Can we now replace $a$ with $\dfrac{dy}{dx}$, and $b$ with $x^2$, and use the information in the question?