" 6."f(x)=sin2x,0

For the function, f(x)=sin2x, 0ltxltpi . Find the point between 0 and pi that satisfies f'(x)=0 .

" If "f(x)={[sin2x,,-2<=x<=0],[ax+b,,0<=x<=2]" ,is differentiable everywhere in "(-2,2)," then "(a,b)" equals."

Let f(x)={{:(,sin2x,0 lt x le xpi//6),(,ax+b,pi//6 lt x lt 1):} If f(x) and f'(x) are continuous, then

If f(x) is defined by f(x)=sin2x, if x =(pi)/(6) Find the values of a and b, if f(x) and f'(x) are continuous at x=(pi)/(6)

Consider f(x)=sin3x,0<=x<=(pi)/(2), then (a) f(x) is increasing for x in(0,(pi)/(6)) and decreasing for x in((pi)/(6),(pi)/(2)) (b) f(x) is increasing forx in(0,(pi)/(4)) and decreasing for x in((pi)/(4),(pi)/(2)) (c) f(x)

Suppose that F (x) is an antiderivative of f (x)=sinx/x,x>0 , then int_1^3 (sin2x)/x dx can be expressed as

Maximum value of f(x)=x+sin2x,x in [0,2pi] is

If f(x)=(4+sin2x+a sinx+Bcosx)/(x^(2)) for x!=0 is continuous at x=0 , then A+B+f(0) is

If f(x)=(4+sin2x+a sinx+Bcosx)/(x^(2)) for x!=0 is at x=0 , then A+B+f(0) is