Find the critical points of: f(x,y)=ex−y -None −(−1,1) &amp; (1,−1) −(t,t):t∈R (t,−t):t∈R

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Wotzdorfg

2021-06-06

Find the critical points of: $f (x, y) = e^{x - y}$
-None
$- (- 1, 1) & (1, - 1)$
$- (t, t) : t \in R$
$(t, - t) : t \in R$

falhiblesw

Skilled2021-06-07Added 97 answers

Step 1
Given function is

f (x, y) = e^{x - y}

To find the partial derivatives of the given function

f_{x} (x, y) = e^{x - y} (1) = e^{x - y}

f_{y} (x, y) = e^{x - y} (- 1) = - e^{x - y}

Step 2
Solving the partial derivatives
solving for x in

f_{x} (x, y) = 0

\Rightarrow e^{x - y} = 0

a^{f (x)}

cannot be zero or negative for x belongs to R
No solution for

x \in R

solving for y in

f_{y} (x, y) = 0

\Rightarrow e^{x - y} = 0

a^{f (y)}

cannot be zero or negative for y belongs to R
No solution for

y \in R

therefore there is no critical point for the given function.

Jeffrey Jordon

Expert2021-12-25Added 2605 answers

Answer is given below (on video)

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