15. `f(x)=min {1, cos 1, 1- sin x},` (A) f(x) is not differentiable at `pi/2 ` (B) f(x) is differentiable at `pi/2` (C) f (a) has local maximum at '0' (D) None of these (D)

If f(x) = x^(3) sgn (x), then A. f is differentiable at x = 0 B. f is continuous but not differentiable at x = 0 C. f'(0^(-)) = 1 D. None of these

If f(x) = x^(3) sgn (x), then A. f is differentiable at x = 0 B. f is continuous but not differentiable at x = 0 C. f'(0^(-)) = 1 D. None of these

Let f(x)=|sinx| . Then, (a) f(x) is everywhere differentiable. (b) f(x) is everywhere continuous but not differentiable at x=n\ pi,\ n in Z (c) f(x) is everywhere continuous but not differentiable at x=(2n+1)pi/2 , n in Z . (d) none of these

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)={{:(,-x-(pi)/(2),x le -(pi)/(2)),(,-cos x,-(pi)/(2) lt x le 0),(,x-1,0 lt x le 1),(,"In "x,x gt 1):} then which one of the following is not correct?(a)f(x) is continuous at x = - (pi)/(2) (b)f(x) is not differentiable at x = 0 (c)f(x) is differentiable x = 1 (d) none of them

Let f(x)=|cosx| (a) Then, f(x) is everywhere differentiable (b) f(x) is everywhere continuous but not differentiable at x=npi,\ \ n in Z (c) f(x) is everywhere continuous but not differentiable at x=(2n+1)\ pi/2,\ \ n in Z (d) none of these

The f(x)=|cosx| (a)Then, f ( x ) is everywhere differentiable at x=(2n+1)\ pi//2,\ \ n in Z (b) continuous but not differentiable at x=(2n+1)\ pi//2,\ n in Z (c) neither differentiable nor continuous at x=npi,\ \ n in Z (d) none of these

f(x) = min{2 sinx, 1- cos x, 1} then int_0^(pi)f(x) dx is equal to

The function f(x)=|cos x| is differentiable at x=(2n+1)pi/2,n in Z(b) continuous but not differentiable at x=(2n+1)pi/2,n in Z(c) neither differentiable nor continuous at x=n pi,n in Z(d) none of these

Let f(x)=|sin x|. Then,(a) f(x) is everywhere differentiable.(b) f(x) is everywhere continuous but not differentiable at x=n pi,n in Z(c)f(x) is everywhere continuous but not differentiable at x=(2n+1)(pi)/(2),n in Z.( d) none of these