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Question Number 165746 by Eric002 last updated on 07/Feb/22

compute the extreme points of:   f=e^x sin(x+y)

$${compute}\:{the}\:{extreme}\:{points}\:{of}:\: \\ $$$${f}={e}^{{x}} {sin}\left({x}+{y}\right) \\ $$

Answered by TheSupreme last updated on 07/Feb/22

y=0  f(x,0)=e^x sin(x)  f(k(π/2))=(−1)^k e^(kπ)   lim_k f(k(π/2))=±∞

$${y}=\mathrm{0} \\ $$$${f}\left({x},\mathrm{0}\right)={e}^{{x}} {sin}\left({x}\right) \\ $$$${f}\left({k}\frac{\pi}{\mathrm{2}}\right)=\left(−\mathrm{1}\right)^{{k}} {e}^{{k}\pi} \\ $$$${li}\underset{{k}} {{m}f}\left({k}\frac{\pi}{\mathrm{2}}\right)=\pm\infty \\ $$

Commented by Eric002 last updated on 07/Feb/22

why did you assume y=0 ??

$${why}\:{did}\:{you}\:{assume}\:{y}=\mathrm{0}\:?? \\ $$

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