Let `f(x)`=`{{:(min{x, x^(2)}, x >= 0),(max{2x, x^(2)-1}, x < 0):}` then
(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

Assertion (A) :f(x) =[x] is not differentiable at x=2. Reason (R ) f(x)=[x] is not continuous at x=2.

If f(x)={ax^(2)+b,x 1;b!=0, then f(x) is continuous and differentiable at x=1 if

Let f(x)=max{1-x,1+x,2}. Prove that f(x) is continuous at all points but notdifferentiable at x=1 and x=-1

Let f(x)=(lim)_(x rarr oo)sum_(r=0)^(n-1)x/((r x+1){(r+1)x+1}) . Then (A) f(x) is continuous but not differentiable at x=0 (B) f(x) is both continuous but not differentiable at x=0 (C) f(x) is neither continuous not differentiable at x=0 (D) f(x) is a periodic function.

Assertion (A) : f(x) = xsin ((1)/(x)) is differentiable at x=0 Reason (R): F(x)is continuous at x=0

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

Let f(x)={{:(,(1)/(|x|),"for "|x| gt1),(,ax^(2)+b,"for "|x| lt 1):} If f(x) is continuous and differentiable at any point, then

Let f(x) ={{:( ( 2x-1) "," ,"when" , x ge 1),( x",", "when", 0 le x le 1):} Show that f(x) is continuous but not differentiable at x =1

If f(x)=2x+|x-x^(2)|,-1<=x<=1 ,then f(x) is is(a) continuous but not differentiable in [-1,1]