Question

Given derivatives how do you find the equation? Problem in comments

Answer 1

saying we have \(P(x) = ax^2+bx+c\), we have \(P'(x)=2ax+b\) and \(P''(x)=2a\)

we are given that \(P''(1)=8\) So that means \(2a = 8\)

We can find a. You should get \(a = 4\).

Then we have \(P'(x) = 8x+b\)

We are given that \(P'(1) = 6\) So you have \(P'(1) = 8(1)+b=6\)

Solve for b.

See what I did here? Can you solve for c then find \(P(x)\) now you have value for \(a\), \(b\) and \(c\)?

Answer 2

I figured out what I did wrong. I put p"(x)=8a making a=1 which messed up the rest of the problem. Thank you :)

Answer 3

Ok, no problem