### Home > APCALC > Chapter 12 > Lesson 12.1.1 > Problem12-12

12-12.

Write the equation of a third-degree polynomial function $f$ such that $f(0) = 7$, $f ′(0) = -3$, $f^{\prime\prime}(0) = 18$, and $f^{\prime\prime\prime} (0) = -30$.

$f(x)=ax^3+bx^2+cx+d$

Use $f(0)$ to solve for $d$.

$f^\prime(x)=3ax^2+2bx+c$

Use $f^{\prime}(0)$ to solve for $c$.