- #1

- 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.

- Thread starter dexza666
- Start date

- #1

- 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

- 3,346

- 5

- #3

- 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

- 3,346

- 5

- #5

- 4

- 0

- #6

Gib Z

Homework Helper

- 3,346

- 5

- #7

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 956

I also want to point out that

1) this is clearly homework

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

- Last Post

- Replies
- 1

- Views
- 2K

- Last Post

- Replies
- 8

- Views
- 3K

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 6

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 2K

- Replies
- 5

- Views
- 3K

- Last Post

- Replies
- 6

- Views
- 2K

- Last Post

- Replies
- 9

- Views
- 5K

- Last Post

- Replies
- 3

- Views
- 1K

- Last Post

- Replies
- 4

- Views
- 1K