[(111)f(x)=cos2x in[-pi/4,pi/4]],[(1v)f(x)=e^(x)sin x on[0,pi]],[(v)f(x)=sin x-sin2x in[0,pi]]

Verify Rolle's theorem for each of the following functions: (i) f(x) = sin 2x " in " [0, (pi)/(2)] (ii) f(x) = (sin x + cos x) " in " [0, (pi)/(2)] (iii) f(x) = cos 2 (x - (pi)/(4)) " in " [0, (pi)/(2)] (iv) f(x) = (sin x - sin 2x) " in " [0, pi]

Verify Rolle's theorem for each of the following functions on indicated intervals; f(x)=sin^(2)x on 0<=x<=pi f(x)=sin x+cos x-1 on [0,(pi)/(2)]f(x)=sin x-sin2x on [0,pi]

If f(x)=e^(x) sin x, x in [0, pi] , then

If f(x)=sin x/ e^(x) in [0,pi] then f(x)

If f(x)=sqrt(1-sin2x), then f'(x) is equal to -(cos x+sin x), for x in((pi)/(4),(pi)/(2))cos x+sin x, for x in(0,(pi)/(4))-(cos x+sin x), for x in(0,(pi)/(4))cos x-sin x, for x in((pi)/(4),(pi)/(2))

If f(x)=cos x+sin x, find f((pi)/(2))

Consider a function fdefined by f(x)=sin^(-1)sin((x+sin x)/(2))AA x in[0,pi] which satisfies f(x)+f(2 pi-x)=pi AA x in[pi,2 pi] and f(x)=f(4 pi-x) for all x in[2 pi,4 pi] then If alpha is the length of the largest interval on which f(x) is increasing,then alpha=

If f(x)=sqrt(1-sin2x) , then f^(prime)(x) is equal to (a) -(cosx+sinx) ,for x in (pi/4,pi/2) (b) cosx+sinx ,for x in (0,pi/4) (c) -(cosx+sinx) ,for x in (0,pi/4) (d) cosx-sinx ,for x in (pi/4,pi/2)

If f(x)=sqrt(1-sin2x) , then f^(prime)(x) is equal to (a) -(cosx+sinx) ,for x in (pi/4,pi/2) (b) cosx+sinx ,for x in (0,pi/4) (c) -(cosx+sinx) ,for x in (0,pi/4) (d) cosx-sinx ,for x in (pi/4,pi/2)