- #1

dexza666

- 4

- 0

tough one

find all critical points of

f(x, y)=e^x(1-cos y)

and classify these critical points.

find all critical points of

f(x, y)=e^x(1-cos y)

and classify these critical points.

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- Thread starter dexza666
- Start date

- #1

dexza666

- 4

- 0

tough one

find all critical points of

f(x, y)=e^x(1-cos y)

and classify these critical points.

find all critical points of

f(x, y)=e^x(1-cos y)

and classify these critical points.

- #2

Gib Z

Homework Helper

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- #3

dexza666

- 4

- 0

\\

\\\frac{\partial f}{\partial x} = e^x(1-\cos y),\ \ \frac{\partial f}{\partial y} = e^x\sin y

\\

\\ e^x(1-\cos y) = 0

\\ \cos y = 1

\\ y = 2k\pi,\ k\in\mathbb{Z}

\\

\\ e^x\sin y = 0

\\ \sin y = 0

\\ y = k\pi,\ k\in\mathbb{Z}

\\

\\\mbox{critical points along the lines }\ y = 2k\pi,\ k\in\mathbb{Z}

\\\mbox{which coincidentaly, is also the lines at which f(x,y) = 0}

\\

is this right

- #4

Gib Z

Homework Helper

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- #5

dexza666

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- 0

- #6

Gib Z

Homework Helper

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- #7

HallsofIvy

Science Advisor

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I also want to point out that

1) this is clearly homework

2) you showed NO attempt to do this in your original post.

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