Find the coordinates of the stationary point of the curve $\displaystyle y=e^xcosx$ for 0 is less than or equal to x and x is less than or equal to $\displaystyle /pi$ . Leave your answer in exact form.

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- Jun 9th 2010, 12:54 AMPunchStationary point...
Find the coordinates of the stationary point of the curve $\displaystyle y=e^xcosx$ for 0 is less than or equal to x and x is less than or equal to $\displaystyle /pi$ . Leave your answer in exact form.

- Jun 9th 2010, 12:58 AMmr fantastic
- Jun 9th 2010, 12:59 AMPunch
$\displaystyle

dy/dx=-e^xsinx

$

am stucked at the part solving for x - Jun 9th 2010, 01:03 AMmr fantastic
- Jun 9th 2010, 01:09 AMPunch
$\displaystyle \frac{dy}{dx} = e^xcosx-e^xsinx$

$\displaystyle = e^x[cosx-sinx]$

now, $\displaystyle e^x[cosx-sinx]=0$ stucked ==" - Jun 9th 2010, 01:12 AMmr fantastic
Correct.

Now solve $\displaystyle \frac{dy}{dx} = 0 \Rightarrow \cos x - \sin x = 0 \Rightarrow 1 = \tan x$ over the given domain.

Then find the y-coordinate corresponding to the solutions for x found above.

If you need more help, please show all your work and say where you get stuck. - Jun 9th 2010, 01:27 AMPunch
i dont understand the part where u "threw" e^x away... wont u lose a solution? other than this everything else is fine :) thx

- Jun 9th 2010, 06:57 PMmr fantastic