# Thread: Stationary points of a Multivariate function

1. ## Stationary points of a Multivariate function

How do I find the stationary points. I find the constants making it difficult to simplify?
And what does part c mean?

This is my working so far.

2. ## Re: Stationary points of a Multivariate function

I do not get $y= \left(\frac{5}{a}\right)^{\frac{1}{1- a}}x$.

From $5y- ax^{a- 1}y^a= 0$, $5y= ax^{a-1}y^a$.

Divide both sides by $y^a$; $5y^{1-a}= ax^{a- 1}$.

Divide by 5: $y^{1- a}= \frac{a}{5}x^{a- 1}$.

Take the 1- a root: $y= \left(\frac{a}{5}\right)^{\frac{1}{1- a}}x^{\frac{a-1}{1-a}}= \left(\frac{a}{5}\right)^{\frac{1}{1- a}}x^{-1}$.

That is, $x^{-1}$, not $x$.

3. ## Re: Stationary points of a Multivariate function

And how would you do part c, which needs to find a hyperbola?

..