Show that `|x-1 | + |x-2|` is not derivable at x = 2

Find the right hand derivative and the left hand derivative of f(x)=x-1,x =2 at the point x=2 and hence show that f(x) is not differentiable at x=2 .

Let f(x) = {{:(( 2+x)",",if , x ge0), (( 2-x)",", if , x lt 0):} show that f(x) not 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

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

Show that the function defined by: f(x) : {:{(3-2x,ifx<2),(3x-7,ifxge2):} is not derivable at x =2.

Find the derivative of x^2 at x = 1.

What is the derivative of |x-1| at x = 2?

Let f(x) = {:{(x+a, x le1),(ax^2 + 1, x > 1):} . Show that f is continuous at 1. Find 'a' so that it is derivable at 1.