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Stationary points of y=-sinx+cosx

by pip_beard
Tags: cosx, points, stationary, ysinx
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pip_beard
#1
Feb8-10, 04:46 PM
P: 14
1. The problem statement, all variables and given/known data
Solve the stationary points of y=-sinx+cosx for domain -pi<x<pi


2. Relevant equations



3. The attempt at a solution
Differentiate: d/dx=cosx+sinx But how do i solve?
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boboYO
#2
Feb8-10, 04:50 PM
P: 104
cosx+sinx=0
cosx=-sinx
1=-tanx??
pip_beard
#3
Feb8-10, 05:01 PM
P: 14
ive got the answers as.. (-pi/4,-rt2) and (3pi/4, rt2) Are the answers wrong?

I dont know how they got these??

because surly the x co-ordinate is 0???

Mark44
#4
Feb8-10, 05:06 PM
Mentor
P: 21,216
Stationary points of y=-sinx+cosx

Quote Quote by pip_beard View Post
1. The problem statement, all variables and given/known data
Solve the stationary points of y=-sinx+cosx for domain -pi<x<pi


2. Relevant equations



3. The attempt at a solution
Differentiate: d/dx=cosx+sinx But how do i solve?
If y = -sinx + cosx, what is dy/dx? Note that it is incorrect to say "d/dx = ..."

If you meant dy/dx = ..., you have made a mistake. Try again.

Also, your notation is not correct. d/dx is an operator that is written to the left of some function. In contrast, dy/dx is the derivative of y with respect to x.
Mark44
#5
Feb8-10, 05:09 PM
Mentor
P: 21,216
Quote Quote by pip_beard View Post
because surly the x co-ordinate is 0???
Why would you think this?
pip_beard
#6
Feb8-10, 05:10 PM
P: 14
so therefore:

dy/dx=cosx+sinx.

stationary points when diff = 0

so cosx+sinx=0 where do i go from here??
pip_beard
#7
Feb8-10, 05:11 PM
P: 14
Quote Quote by Mark44 View Post
Why would you think this?
because stationary points lie on the x axis??
Mark44
#8
Feb8-10, 07:25 PM
Mentor
P: 21,216
Quote Quote by pip_beard View Post
because stationary points lie on the x axis??
x-values lie on the x-axis, but stationary points lie on the curve, which might not even touch the x-axis. For example, the only stationary point on the graph of y = x^2 + 1 is at (0, 1). This is not a point on the x-axis.
Mark44
#9
Feb8-10, 07:28 PM
Mentor
P: 21,216
Quote Quote by pip_beard View Post
so therefore:

dy/dx=cosx+sinx.
No, dy/dx = -cosx - sinx

To find the stationary points, set dy/dx to zero.
-cosx - sinx = 0
==> cosx + sinx = 0
==> 1 + tanx = 0 (dividing both sides by cosx)
Can you continue?

Quote Quote by pip_beard View Post

stationary points when diff = 0

so cosx+sinx=0 where do i go from here??


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