A function f(x) having the following properties (i) f(x) is continuous except at `x= 3` (ii) f(x) is differentiable except at `x =-2` and `x = 3`

Consider the following in respect of the function f(x)=|x-3| . I. f(x) is continuous at x = 3 II. F(x) is differentiable at x = 0 Which of the above statement us/are correct?

If f(x) = 3(2x + 3)^(2//3) + 2x + 3 , then: (a) f(x) is continuous but not differentiable at x = - (3)/(2) (b) f(x) is differentiable at x = 0 (c) f(x) is continuous at x = 0 (d) f(x) is differentiable but not continuous at x = - (3)/(2)

Show that the function f defined as follows f(x)={3x-2, 0 2 is continuous at x=2 , but not differentiable thereat.

Show that the function f defined as follows f(x)={3x-2, 0 2 is continuous at x=2 , but not differentiable thereat.

Show that the function f(x)=x|x| is continuous and differentiable at x = 0

Let f(x)={ax(x-1)+b;x 3 is contnuous AA x in R except x-1 and |f(x)| is differentiable every where and f'(x) is continuous at x=3.

Show that the function f(x) =x^2 is continuous and differentiable at x=2.

Show that the function f(x) =x^2 is continuous and differentiable at x=2.

Consider the following statements: I. f(x)=|x-3| is continuous at x=0. II. f(x)=|x-3| is differentiable at x=0. Which of the statements given above is/ are corrent?