The discussion revolves around finding the stationary points of the function y = -sin(x) + cos(x) within the domain -π < x < π. Participants are exploring the process of differentiation and the conditions under which stationary points occur.
The discussion is ongoing, with participants providing various interpretations and corrections regarding the differentiation process. Some guidance has been offered on the proper notation and the concept of stationary points, but no consensus has been reached on the specific stationary points or their coordinates.
There is some confusion regarding the notation used for differentiation and the relationship between stationary points and their positions relative to the x-axis. Participants are also questioning assumptions about the nature of stationary points in relation to the function's graph.
If y = -sinx + cosx, what is dy/dx? Note that it is incorrect to say "d/dx = ..."pip_beard said:Homework Statement
Solve the stationary points of y=-sinx+cosx for domain -pi<x<pi
Homework Equations
The Attempt at a Solution
Differentiate: d/dx=cosx+sinx But how do i solve?
Why would you think this?pip_beard said:because surly the x co-ordinate is 0?
Mark44 said:Why would you think this?
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.pip_beard said:because stationary points lie on the x axis??
No, dy/dx = -cosx - sinxpip_beard said:so therefore:
dy/dx=cosx+sinx.
pip_beard said:stationary points when diff = 0
so cosx+sinx=0 where do i go from here??