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Find the critical points?

0 votes

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)

asked Jul 22, 2014 in PRECALCULUS by anonymous

1 Answer

0 votes

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

First find the first order partial derivatives.

Vx = - (0.017y - 0.2)e- 0.2x sin(0.017y - 0.2x) - 0.2e- 0.2xcos(0.017y - 0.2x)

Vy = - (0.017 - 0.2x)e- 0.2x sin(0.017y - 0.2x).

Solve the following equations  Vx = 0  and Vy = 0 simultaneously.

Vx = - e- 0.2x[(0.017y - 0.2)sin(0.017y - 0.2x) + 0.2cos(0.017y - 0.2x)] = 0

Vy = - (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

answered Jul 25, 2014 by lilly Expert

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