AP Calculus 1990 #5?

Question

Let f be the function defined by f(x) = (sinx)^2-sinx for 0
(a) find the x-intercepts of the graph of f
(b) find the intervals on which f is increasing
(c) find the absolute maximum value and the absolute minimum value of f.

Answer 1

sin^2x-sinx= 0 sinx= 0 and sin x=1 so x=0 x=pi and x=pi/2
f´(x)= 2six cosx -cos x = cos x(2sin x-1)=0
cos x= 0 x= pi/2 and 3pi/2 sinx=1/2 x= pi/6 and x= 5pi/6
The values of the function at those points are
0,0,2-1/4,-1/4
The abs max is 2 at x=3pi/2 and the abs min -1/4 at x=pi/6 and x=5pi/6
sign of f´(x)

cosx ++++++pi/2-----------------3pi/2
2sinx-1 ------pi/6+++++++++++5pi/6-----3pi/2

pi/6<=x<= pi/2 and 5pi/6<=x<=3pi/2 f(x) is increasing