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| 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

f(x)={(x^2+2x, "" xle0,),(ax+b, "" x >0,):} is continuous and differentiable at x =0, find the values of a and b

If f(x)={(1-cosx)/(xsinx),x!=0 and 1/2,x=0 then at x=0,f(x) is (a)continuous and differentiable (b)differentiable but not continuous (c)continuous but not differentiable (d)neither continuous nor differentiable