Asked by Galagan
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).
(a) Calculate local maxima/minima and points of in
ection of f(x).
Answers
Answered by
Reiny
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
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
Answered by
Galagan
How do you get the point of inflections?
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