Originally Posted by

**slaypullingcat** a) given y=e^-x cos x I found y'=-e^-x(sin x + cos x) and

y"=2e^-x(sin x). I checked and they are right.

b) find stationary points between -pi<x<pi and determine their nature.

I can do this with simple quadratics but this function is beyond me at present.

$\displaystyle \textcolor{red}{-e^{-x}(\sin{x} + \cos{x}) = 0}$

$\displaystyle \textcolor{red}{-e^{-x}}$ is always negative ... that means

$\displaystyle \textcolor{red}{\sin{x} = -\cos{x}}$ ... now, for what two values of x in the defined interval is that true?

c) Find the points of inflection for -pi < x < pi

$\displaystyle \textcolor{red}{2e^{-x}\sin{x} = 0}$

same idea ... the only place where y'' = 0 in the given interval is at the endpoints and x = 0 .