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.

Explain whether f(x) is continuous and has a derivative at the point x=1 were f(x)=x for 0 1

f(x)=xabsx is derivable at x=0 .

Suppose that 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

Examine whether the function f(x)=x^2 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