Consider the function f : [􀀀-pi,pi] -- R given by f(x) = e􀀀^-x*sin(x).

Question

Consider the function f : [􀀀-pi,pi] --> R given by f(x) = e􀀀^-x*sin(x).
(a) Calculate local maxima/minima and points of in
ection of f(x).

Reiny · Answer

Let's see what this looks like
https://www.wolframalpha.com/input/?i=plot+y+%3D++%28e%5E-x%29%28sin%28x%29%29

f ' (x) = e^-x(cosx) - sinx (e^-x)
= 0 for max/min

e^-x(cosx - sinx)=0
e^-x = 0 ---> not possible
or
cosx = sinx
tanx = 1

x = pi/4 or -3pi/4

sub that back in original to find the corresponding max/min

Galagan · Answer

How do you get the point of inflections?

Consider the function f : [􀀀�-pi,pi�] --> R given by f(x) = e􀀀^-x*sin(x).