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.
...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
cosx<=0 implies that pi/2<=x<=3*pi/2
and sinx<=1/2. implies ...