If f(x)={ax2+bb≠0, x≤1bx2+ax+cx>1  then f(x)  is continuous and differentiable at x=1  if

Since, f(x)  is continuous at x=1 ∴ limx→1−f(x)=limx→1+f(x) ⇒  a+b=b+a+c ⇒  c=0 As ⇒  c=0 As f(x)  is differentiable at x=1 ∴  (LHD at x=1)=(RHD at x=1) ⇒  2a+0=2b+a+0 ⇒ a=2b ∴ a=2b, c=0