Review question

# When does this function of two variables have a minimum? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9671

## Suggestion

The variables $x$ and $y$ are such that $x^4y=8$. A third variable $z$ is defined by $z=x+y$.

Find the values of $x$ and $y$ that give $z$ a stationary value…

This looks tricky as $z$ is given as a function of two variables. Can we use the equation connecting $x$ and $y$ to turn $z$ into a function of just one variable?

How do we then calculate stationary points for $z$?

… and show that this value of $z$ is a minimum.

What does the second derivative tell us about a stationary point?