# Thread: critical points of a function

1. ## 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 $u(x,y) = e^{y^2-sinx}$.

2. Originally Posted by maximus101
(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 $u(x,y) = e^{y^2-sinx}$.
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.