are there any other maxima or minima of y=x+sinx other than when x=pi?

Question

in the interval of [-pi/2, 3pi/2] for x

Answer 1

1) As x may have any value, there aren't maxim or minim,

2) If x = pi
pi + sin p = one only value. So there aren't maxim or minim either.

Answer 2

There are no maxima or minima over the the entire domain of x. There are only points of inflection where the concavity changes

In fact as x --> infinity, f(x) -> x. sinx oscillates between 1and -1 so it become insignificant.

Answer 3

Well, maxima and minima are points of inflection. So, following my answer to your previous question, they exist when dy/dx = 0

In this case, dy/dx = 1 + cos x

So any maxima/minima will occur when cos x = -1, with x in the range you specified.

Edit: oops, I had the sign wrong on the cos... corrected.

Answer 4

nope, x=pi is the only time that cos(x)+1=0 in the interval you've given. (ie cos(x)+1 being your derivative)

note that the period of the cos function is 2pi, and the range you've given equates to 2pi, so it is correct that cos takes on the value of -1 only once in this range.