Mathematica 9: how to solve a maximization?

Question

How can I maximize the following equation in respect to $\tau$ in Mathematica 9:

$$max_\tau \sqrt{(1 - \tau)y^i} + \sqrt{\tau y}$$

I want to find something like

$$\tau^i = \frac{y}{y^i + y}$$

Answer 1

Let x = Τ then f(x, y) = sqrt((1-x)*y^c) + sqrt(xy)

I'll assume that c is a constant, so there are only two independent variables here.

So take the first partial derivative w.r.t. x and set that equal to zero.

Wolfram Alpha can help you with that.