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

Show that the function defined by f(x) = {{:(x^(2) sin 1//x",",x ne 0),(0",",x = 0):} is differentiable for every value of x, but the derivative is not continuous for x =

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)={1/(1+e^((1,)/x)),x!=0 0,x=0,t h e nf(x) is continuous as well as differentiable at x=0 continuous but not differentiable at x=0 differentiable but not continuous at x=0 none of these

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

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

The function f(x)=|x|+|x-1| is Continuous at x=1, but not differentiable at x=1 Both continuous and differentiable at x=1 Not continuous at x=1 Not differentiable at x=1

If f(x)={(1)/(1+e^(1/x)),quad x!=00,quad x=0 then f(x) is continuous as well as differentiable at x=0 (b) continuous but not differentiable at x=0 (c) differentiable but not continuous at x=0 (d) none of these

If f(x) ={ (x.ln(cosx))/ln (1+x^2) x!=0 , 0, x=0 then a) f is continuous at x =0 b) f is continuous at x =0 but not differentiable at x=0 c) f is differemtiable at x =0 d) f is not continuous at x =0

If f(x)={xe^-(1/|x|+1/x) , x!=0 ,, 0, x=0 (1) discontinuous everywhere(2) continuous as well as differentiable for all x(3) continuous for all x but not differentiable at x=0(4) neither differentiable nor continuous at x = 0