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
$$\tau^i = \frac{y}{y^i + y}$$
Mathematica 9: how to solve a maximization?
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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.