If `y=f(x)` is differentiable at `x=a`; then it is not necessary that the derivative is continuous at `x = a`

if a function f(x) is differentiable at x=c then it is also continuous at x=c

If f(x)=|3-x|+(3+x), where (x) denotes the least integer greater than or equal to x , then f(x) is continuous and differentiable at x=3 continuous but not differentiable at x=3 differentiable but not continuous at x=3 neither differentiable nor continuous at x=3

If f(x)=|3-x|+(3+x), where (x) denotes the least integer greater than or equal to x, then f(x) is continuous and differentiable at x=3 continuous but not differentiable at x=3 differentiable but not continuous at x=3 neither differentiable nor continuous at x=3

If a function f(x) is differentiable at x = c prove that it is continuous at x = c.

"Let "f(x)=phi(x)+Psi(x) where, phi'(x) and Psi'(x) are finite and definite. Then, a. f(x) is continuous at x = a b. f(x) is differentiable at x = a c. f'(x) is continuous at x = a d. f'(x) is differentiable at x = a

If f(x)=|3-x|+(3+x), where (x) denotes the least integer greater than or equal to x, then f(x) is continuous and differentiable at x=3 (b) continuous but not differentiable at x=3 (b) differentiable but not continuous at x=3 (d) neither differentiable nor continuous at x=3

Suppose f(x) is differentiable at x=a . Then , necessary condition for f(x) to possess local maxima or local minima at x=a is

Let f(x) = {{:(min{x, x^(2)}, x >= 0),(max{2x, x^(2)-1}, x (A) f(x) is continuous at x=0 (B) f(x) is differentiable at x=1 (C) f(x) is not differentiable at exactly three point (D) f(x) is every where continuous

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)

If f(x)=|3-x|+[3+x] , where [x] denotes the least integer greater than or equal to x , then f(x) is:(a) continuous and differentiable at x=3. (b) continuous but not differentiable at x=3. (c)differentiable but not continuous at x=3. (d)neither differentiable nor continuous at x=3..