# Trig Functions: Intercepts, Intervals, and Maximum and Minimum

Let f be the function defined by f(x)=sin squared x - sinx for 0<or=x<or=(3pi)over 2.

a. find the x- intercepts of the graph of f

b.find the intervals on which f is increasing

c. find the absolute maximum and absolute minimum value of f. Justify your answer.

#### Solution Preview

...dn't mention the range of x in your problem) in

general x=k*pi for k=0,1,2,..

or x=pi/2, or in general x=2k*pi+pi/2 for k=0,1,2...

b. .find the intervals on which f is increasing is to.find the intervals such that

f'(x)> or =0. Now

f'(x)=2sinx cosx-cosx=cosx(2sinx-1). Thus we need to find x such that

cosx>=0 and sinx>=1/2. or

cosx<=0 and sinx<=1/2.

cosx>=0 , we have 0<=x<=pi/2 or 3*pi/2<=x<=2*pi

sinx>=1/2, we have pi/6<=x<=5*pi/6.

Thus in order that cosx>=0 and sinx>=1/2 , we need

pi/6<=x<=pi/2. Now

cosx<=0 implies that pi/2<=x<=3*pi/2

and sinx<=1/2. implies ...