Hello, Confucius!

Use Lagrange multipliers to find the point(x, y)on the graph y=e^{x}, where the valuexyis as small as possible.

We want to minimize: subject to the constraint:

We have: .

Set the partial derivatives equal to zero, and solve.

. .

From [2]: .

Substitute into [1]: .

Substitute into [3]: .

. . . . . . . . . . . . . . . . .

Substitute into [3]: .

Therefore: .