A function f (x) is defined by :
`f(x)={(px^2+1,"for"xlt1),(x+p,"for"xgt1):}`
if f (x) be differentiable at x = 1 then p =

Define f(x)={{:(x^2+bx+c,","xlt1),(x,","xge1):} } .If f(x) is differentiable at x=1 , then (b-c)=

A function f (x) is defined as follows : f(x)={{:(3x+1,"for "xle1 ),(3-ax^(2),"for " xgt1):} If f (x) is continuous at x = 1 , find the value of a.

Is the function f , defined by f(x)={{:(x^(2),"if "xle1),(x,"if "xgt1):} continuous on R ?

The function f is defined by f(x)={{:(x+3" if ",xlt1),(x^(2)" if ",xge1):} . Find f(-5),f(1), and f(3) .

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 .

A function f (x) is defined as follows : f(x)={{:(2-x",","when "xlt1),(x^(2)-3x",","when "xge1):} Examine the differentiability of the function f (x) at x= 1 , hence state whether f (x) is continuous at x = 1 or not .

Find 'a' and 'b', if the function given by: f(x)={{:(ax^(2)+b", if "xlt1),(2x+1", if "xge1):} is differentiable at x = 1.

The function f(x)={(2,xle1),(x,xgt1):} is not differentiable at

Let f(x) be a function defined in 1lexltoo by. f(x)={:[(2-x,"for "1lexle2),(3x-x^(2),"for "xgt2):} What is the differentiable coefficient of f(x) at x = 3?