Calculus Help Anyone?

Question

Find all relative extrema and points of inflection for

f(x) = x - sinx

over the interval
0

Answer 1

To find maxima, minima and point of reflections,

method:
Take derivative. See at what points it becomes 0.
Find 2nd derivative.

If second derivative is positive it is minima
If second derivative is negative it is maxima
If second derivative is zero it is point of reflection.


I think you can solve it now.
Thank you.

Answer 2

f(x) = x - sinx
f'(x) = 1 - cosx
f''(x) = sinx
For possible relative max and min
cosx = 1
x = 0, 2π, 4π
For inflection points
sinx = 0
x = 0, π, 2π, 3π, and 4π
so none of the points of 0 slope is a max or min