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)={:{(1+sin x", " 0 le x lt pi//2),(" "1 ", " x lt0):} then show that f'(0) does not exist.

Let f(x)={{:(ax-b,","x le 1),(3x,"," 1 lt x lt 2),(bx^2-a,"," x ge 2):} If f is continuous function then (a,b) is equal to

Let f(x) = {{:(sgn(x)+x",",-oo lt x lt 0),(-1+sin x",",0 le x le pi//2),(cos x",",pi//2 le x lt oo):} , then number of points, where f(x) is not differentiable, is/are

Let f(x) = {{:(sgn(x)+x",",-oo lt x lt 0),(-1+sin x",",0 le x le pi//2),(cos x",",pi//2 le x lt oo):} , then number of points, where f(x) is not differentiable, is/are

Let f(x) = {(x "sin" (pi)/(x)",",0 lt x le 1),(0,x =0):} . Then f'(x) = 0 for

f(x)= {(-4 sin x + cos x",",x le - (pi)/(2)),(a sin x + b",",-(pi)/(2) lt x lt (pi)/(2)),(cos x + 2",",(pi)/(2) le x):} . If f(x) is continuous for x in R , then find the value of a and b.