Question

If $p\left(x\right)$ is a polynomial of degree $3$, $p\left(0\right)=4$,$p^{{}^{\prime }}\left(0\right)=3,p^{{}^{\prime \prime }}\left(0\right)=6,p^{{}^{\prime \prime \prime }}\left(x\right)=6$, then $p^{{}^{\prime \prime }}(-1)=$

• A. $10$
• B. $8$
• C. $6$
• D. $0$

Answer 1

The correct option is D $0$

$P\left(x\right)=a{x}^3+b{x}^2+cx+d$
$P^{{}^{\prime }}\left(x\right)=3a{x}^2+2bbx+c$
$P^{{}^{\prime \prime }}\left(x\right)=6ax+2b$
$P^{\prime \prime \prime }\left(x\right)=6a$
$6=6a$
$a=1$
$P^{\prime \prime }\left(0\right)=2b$
$b=3$
$P^{\prime }\left(0\right)=c$
$c=3$
$P^{\prime }\left(0\right)=d$
$d=4$
$P^{\prime \prime }(-1)=-6a+2b=-6\times 1+2\times 3$
$=0$