Examine whether f(x) = `|x|` has a derivative at x = 0.

Examine whether f (x)=|2x| has a derivative at x = 0

Examine whether f(x)=|x+1| has a derivative at x = - 1 .

Given, f'(c) =lim_(xtoc) (f(x)-f(c))/(x-c) , when the limit exists,. Using this difinition investigate whether f(x) =(1)/(x) has a derivative at x = 2 and obtain the derivative, if it exists.

Find the derivative of f(x) = 10x.

If f(x)={{:(x+sinx,"when "xlt0),(0,"when "xge0):} examine whether f(x) is continuous at x = 0.

Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and derivative 7 at x=2 . The derivative of the function f(x)-f(4x) at x=1 has the value equal to (a) 19 (b) 9 (c) 17 (d) 14

A function f(x) is defined as follows : " "f(x)={:{(x-1",","when "x gt 0),(-(1)/(2)",","when "x = 0),( x+1",","when "xlt0):} Draw the graph of the function f(x). From the graph find the value of f(x) at x=-(1)/(2) and examine whether f(x) is continuous at x = 0.

Find the derivative of f(x) = x^(2) .

Sketch the graph of f(x)=|x-4|-2. From the graph examine whether f(x) is continuous at x = 4 or not.

Sketch the graph of the function : f(x)=0," when "x lt1 =x-1," when "x ge1 From the graph examine whether f(x) is continuous at x =1 or not.