If the function
`f(x)={{:(,-x,x lt 1),(,a+cos^(-1)(x+b),1 le xle 2):}` is differentiable at x=1, then `(a)/(b)` is equal to

If f(x)={{:(,ax^(2)-b,|x|lt 1),(,(1)/(|x|),|x| ge1):} is differentiable at x=1, then

If f(x)={{:(,ax^(2)-b,|x|lt 1),(,(1)/(|x|),|x| ge1):} is differentiable at x=1, then

Show that the function f (x) = {{:( x , if x lt 1), ( 3-x , if 1 le x le 3), (x ^(2) - 4x +3, if x gt 3):} is not differentiable at 1,3.

The values of a and b if the function f(x)={{:(x^(2)+3x+a",",xle1),(bx+2",",xgt1):} is differentiable at x =1, are :

Show that the function f (x) = {{:( x, if x lt 1), ( 6 -2x , if 1 le x le 3), ( x ^(2) - 4x + 3, if x gt 3):} is not differentiable at x = 1,3

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