# How do you use lagrange multipliers to find the point (a,b) on the graph y=e^(3x) where the value ab is as small as possible?

Mar 6, 2015

You rewrite the problem in more useful form.

We usually express these problems as:
Minimize: (objective function)
Subject to: (constraint equation)

You want to minimize the product of two number, so the objective function is $f \left(x , y\right) = x y$.
The constraint is $y = {e}^{3 x}$.

So the problem becomes:

Minimize: $f \left(x , y\right) = x y$
Subject to: ${e}^{3 x} - y = 0$

(If you prefer, you could use constraint $y - {e}^{3 x} = 0$)

Now, proceed as usual for a Lagrange multiplier problem.