How do you use lagrange multipliers to find the point (a,b) on the graph y=e^(3x)y=e3x where the value ab is as small as possible?

1 Answer
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(x,y)=xyf(x,y)=xy.
The constraint is y=e^(3x)y=e3x.

So the problem becomes:

Minimize: f(x,y)=xyf(x,y)=xy
Subject to: e^(3x)-y=0e3xy=0

(If you prefer, you could use constraint y-e^(3x)=0ye3x=0)

Now, proceed as usual for a Lagrange multiplier problem.