p(x) is a polynomial of degree 3. Let p(x)=ax3+bx2+cx+d p′′(x)=3ax2+2bx+c p′′(x)=6ax+2b p′′′(x)=6a ∵ p′′(1)=0 and p′′(1)=6 ⇒ 6a+2b=0 ...(i) 6a=6 ⇒a=1 From Eq. (i), we get 6×1+2b=0 2b=−6 ⇒b=−3 ∴ p′′(0)=6a(0)+2b =0+2(−3)=−6