Let `h(x) = min {x, x^2}`, for every real number of X. Then (A) h is continuous for all x (B) h is differentiable for all x (C) `h^'(x)` = 1, for all x > 1 (D) h is not differentiable at two values of x

Let f be a function which is continuous and differentiable for all real x. If f(2)=-4 and f'(x) >= 6 for all x in [2,4], then

If f(x) = {{:(|1-4x^(2)|",",0 le x lt 1),([x^(2)-2x]",",1 le x lt 2):} , where [] denotes the greatest integer function, then A. f(x) is continuous for all x in [0, 2) B. f(x) is differentiable for all x in [0, 2) - {1} C. f(X) is differentiable for all x in [0, 2)-{(1)/(2),1} D. None of these

The function f(x)=(sin(pi[x-pi]))/(4+[x]^2) , where [] denotes the greatest integer function,(a) is continuous as well as differentiable for all x in R (b) continuous for all x but not differentiable at some x (c) differentiable for all x but not continuous at some x . (d) none of these

The function f(x)=(sin(pi[x-pi]))/(4+[x]^2) , where [] denotes the greatest integer function, (a) is continuous as well as differentiable for all x in R (b) continuous for all x but not differentiable at some x (c) differentiable for all x but not continuous at some x . (d) none of these

Let h(x) =f(x)-a(f(x))^(3) for every real number x h(x) increase as f(x) increses for all real values of x if

Let f(x)={1, x =1 . Then, f is (a) continuous at x=-1 (b) differentiable at x=-1 (c) everywhere continuous (d) everywhere differentiable

Let h (x) = min (x, x^2), x in R , then h (x) is

Let f(x) ={{:( xe^(x), xle0),( x+x^(2)-x^(3), xgt0):} then the correct statement is (a) f is continuous and differentiable for all x (b) f is continuous but not differentiable at x=0 (c) f is continuous and differentiable for all x . (d) f ' is continuous but not differentiable at x=0

If f(x)=|(log)_e|x|| , then (a) f(x) is continuous and differentiable for all x in its domain] (b) f(x) is continuous for all x in its domain but not differentiable at x=+-1 (c) f(x) is neither continuous nor differentiable at x=+-1 (d) none of these

The number of points that the functions f(x)= |2x+ 1|+|2x-1| , " for all x " in R is not differentiable is