- #1

dkotschessaa

- 1,060

- 783

## Homework Statement

Find all polynomials of the form a + bx + cx^2 that:Goes through the points (1,1) and (3,3)

and such that f'(2) = 1

## Homework Equations

a + bx + cx^2

f'(x) = x+2cx

f'(2) = 2 + 4c

polynomial through (1,1) = a + b1 + c1 = 1

polynomial through (3,3) = a + b3+ c3^2 = 3

## The Attempt at a Solution

I have the general idea that this should result in a series of equations that I need to do gauss Jordan on. Similar problems like this resulted in 3 similar equations and were quite simple.

My problem here is that, since I have taken the derivative of f(x) I have lost my constant a. So I'm not sure what my matrix should look like. I've tried:

1 1 1 1

1 3 9 3

But for the one with the derivative, my f"(2) isn't in the same form - it's 2+4c = 1

so I"m not sure whether to use

1 2 4 1

0 2 4 1

or something more general. If I use something more general though like:

a 2 4 1

I can't get a pivot in my first column...

'elp!

-Dave K