Question

Find the critical points and test these points for other relevant points for maxima, minima or saddle points.

V(x,y)= e^(-.2x)* cos(.017y-0.2x)

Answer 1

The function V(x, y) = e^{- 0.2x} * cos(0.017y - 0.2x).

First find the first order partial derivatives.

V_x = - (0.017y - 0.2)e^{- 0.2x} sin(0.017y - 0.2x) - 0.2e^{- 0.2x}cos(0.017y - 0.2x)

V_y = - (0.017 - 0.2x)e^{- 0.2x} sin(0.017y - 0.2x).

Solve the following equations  V_x = 0  and V_y = 0 simultaneously.

V_x = - e^{- 0.2x}[(0.017y - 0.2)sin(0.017y - 0.2x) + 0.2cos(0.017y - 0.2x)] = 0

V_y = - (0.017 - 0.2x)e^{- 0.2x} sin(0.017y - 0.2x) = 0

Since exponentials are non zero, this reduces to (0.017 - 0.2x)sin(0.017y - 0.2x) = 0

 0.017 - 0.2x = 0  and  sin(0.017y - 0.2x) = 0

⇒ cos(0.017y - 0.2x) = 0  and  sin(0.017y - 0.2*0.085) = 0

No, such points exists.

Source : https://in.answers.yahoo.com/question/index?qid=20140721090127AAy65Ug