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Math Help - critical points of a function

  1. #1
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    critical points of a function

    (i) Given a function  f: \Re ^2 \rightarrow \Re, define
    u: \Re^2 \rightarrow \Re by u(x,y):= e^{f(x,y)} for all
    (x,y) \in \Re^2.

    Show that u has exactly the same critical points as f.
    (ii) Find all critical points of u(x,y) = e^{y^2-sinx}.
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  2. #2
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    Quote Originally Posted by maximus101 View Post
    (i) Given a function f: \Re ^2 \rightarrow \Re, define <br />
u: \Re^2 \rightarrow \Re by u(x,y):= e^{f(x,y)} for all <br />
(x,y) \in \Re^2.
    Show that u has exactly the same critical points as f.
    (ii) Find all critical points of u(x,y) = e^{y^2-sinx}.
    Your function is u(x,y)= e^{f(x,y)} (what in the world is a "blacklisted command"??)

    \frac{\partial u}{\partial x}= e^{f(x,y)}\frac{\partial f}{\partial x}
    and \frac{\partial u}{\partial y}= e^{f(x,y)}\frac{\partial f}{\partial y}

    and, of course, the exponential is never 0.
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