Question

9. consider the function y=e^-x sin x where pie < x < pie

find dy/dx which is e^-x(cos x - sin x)

show that at stationary points, tan x = 1. - I have done this part

I don't understand this part:
How do I do this: determine the co-ordinates of the stationary points correct to 2 dp.

Could you tell me how to start off this question?

Answer 1

You have show that the condition for stationary points is that tanx = 1

In the next part we actually have to find those points,
that is, solve
tanx = 1
x = 45° or x = 225°
or
x = π/4 or x = 5π/4 radians

when x = π/4
y = e^-π/4 sin π/4 = .3224

when x = 5π/4
y = e^-5π/4 sin 5π/4 = -.011139

Looking at your domain, I think you made a typo, and I will assume you meant
-π < x < π
so the second point above lies outside the domain,
but there is another solution of
x = -135° or -3π/4

if x = -3π/4
y = e^-3π/4 sin 3π/4 = -.067

Within your domain, the stationary points are
(π/4, .3224) and (-3π/4, -.067)