find the values of `a ` and `b` , such that `f(x) ={ax^2+1,xle1 and x^2+ax+b , x gt1` is differentiable at `x=1`

Find the values of p and q , so that f(x)={{:(x^(2)+3x+p, ifxle1),(qx+2,ifx gt1):} is differentiable at x = 1

For what values of a and b, is the function f(x)= {(x^(2) "," x le c),(ax + b"," x gt c):} differentiable at x=c

Find the values of aa n db if f(x)={a x^2+1,xlt=1 ,x^2+a x+b ,x >1"i s differentiable at"x=1

Let f(x) =e^(x-1)-ax^(2)+b and g(x)={{:(e^(x-1),xle1),(x^(2)+1,xgt1):}, then find the values of a and b such that f(x) xx g(x) is differentiable at x=1 .

Find the values of a and b if f(x)={a+sin^(-1)(x+b), xgeq1 and x ,x<1 is differentiable at x=1.

Find the values of a and b if f(x)={a+sin^(-1)(x+b),xgeq1 and x ,x<1 is differentiable at x=1.

Find the values of a and b , if the function f defined by f(x)={x^2+3x+a ; if xlt=1, b x+2 ; if x >1 is differentiable at x=1

Find the values of a and b , if the function f(x) defined by f(x)={x^2+3x+a ,\ \ xlt=1b x+2,\ \ \ \ \ \ \ \ \ \ x >1 is differentiable at x=1 .

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

If f(x)={{:(e^(2x^(3)+x),x gt 0),(ax+b, x le 0):} is differentiable at x = 0, then