lf `f(x) ={ax^2+b ,x leq 1 and bx^2+ax+c , x >1; b != 0`, then `f(x)` is continuous and differentiable at `x = 1` if

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

If function defined by f(x) ={(x-m)/(|x-m|) , x leq 0 and 2x^2+3ax+b , 0 lt x lt 1 and m^2x+b-2 , x leq 1 , is continuous and differentiable everywhere ,

Let f(x)={(1/(|x|), for |x| ge 1),(ax^2+b,for |x| < 1)) . If f(x) is continuous and differentiable at any point, then (A) a=1/2, b=-3/2 (B) a=-1/2, b=3/2 (C) a=1,b=-1 (D) none of these

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) = {{:(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