How do you find the critical points to graph #y=sin (x/2)#?
Critical points for graphing occurs where the curve is maximum, minimum or has zeros. Let us see a trick to find them.
Since the question is about the sine curve, let me put a figure of a sin(x) curve between
The red arrows show where the curve has zero or
The green arrows indicate where the curve got maximum,.
We can see how the curve moves from Zero, max, zero, min and zero.
Each happens at the same interval, if you see carefully it is
We can see the critical points are at
Let us come to our question
The period for
The interval length to find the critical points is
The critical points would be at
The zeros would be at
The maximum would be at
The minimum would be at