Question

3. Given the function defined by y = x + sinx for all x such that -π/2<=x<=3π/2
a. Find the coordinate of all maximum and minimum points on the given interval. Justify your answers.
b. Find the coordinates of all points of inflection on the given interval. Justify your answers.

please be explisive!
thanks!

Answer 1

dy/dx = 1 + cos x
0 when cos x = -1
that is when x = pi

d^2y/dx^2 = -sin x
-sin x = 0 when x = pi
so this is not a max or min but a point of inflection

Answer 2

now look at the ends
at x = - pi/2
y = - pi/2 + sin(-pi/2) = -pi/2 -1
minimum I bet

at x = 3 pi/2
y = 3 pi/2 + sin (3 pi/2) = 3 pi/2 -1
maximum