Examine the differentiability of f(x) `= 2x^(2)+ 1 ` at x = 1 .

Examine the differentiability of f(x) =2x+|x-1| at x = 1

Examine the continuity and differentiability of f (x) =2x^(2)+1 " at "x=1 .

examine the differentiability of f(x)={[x^(2)+1, if 0<=x<=1],[3-x, if 1<=x<=2] 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 .

Given {:(f(x)=x^(2)-2x+3," ""when "xlt1),(=2," ""when "x=1),(=2x^(2)-5x+5," ""when "x gt1):} Examine the differentiability of the function at x = 1 .

Let f:RtoR (R is the set of real numbers) be defined as follows : f(x)={{:(2-x", for "1lexle2),(x-1/2x^(2)", for "xgt2):} . Examine the continuity and differentiability of f(x) at x = 2.

Examine the differentiability of the function f(x)=|cosx| at x=(pi)/(2) .

Examine the differentiability of f, where f is defined by f(x) = {(x.[x]",","if " 0 le x lt 2),((x-1)x,"if " 2 le x lt 3):} at x= 2