# Thread: find a polynomial function p(2)=5p'(2)=3 and p''(2)=2

1. ## find a polynomial function p(2)=5p'(2)=3 and p''(2)=2

find a polynomial function $p(2)=5$, $p'(2)=3$ and $p''(2)=2$

is this done by trail and error or is there a specific method for solving this?

2. ## Re: find a polynomial function p(2)=5p'(2)=3 and p''(2)=2

let's try a polynomial of minimum possible degree ... 2

$p(x) = ax^2 + bx + c$ ... $5 = 4a + 2b + c$

$p'(x) = 2ax + b$ ... $3 = 4a + b$

$p''(x) = 2a$ ... $2 = 2a$

should be able to find $p(x)$ now ...