Your p'(t) is wrong.
Hi, I thought I knew how to solve this problem, but I don't really understand the answer I got.
The question is as followed:
Find the equation of a cubic polynomial which passes through (1,1), with slope -5 at this point, and through (-1,7), with slope -5 at this point.
So, consider some things...
p(t) = a0 + a1t + a2t^2 + a3t^3
p`(t) = a1 + a2t + a3t^2
p`(1) = -5, p(1) = 1, p(-1) = 7 and p`(-1) = -5
So, I have four linear equations:
a0 + a1 + a2 + a3 = 1, a0 - a1 + a2 - a3 = 7, a1 + a2 + a3 = -5, a1 -a2 + a3 = -5
So, I decided to plug these equations into my ti-89 and rref it.
1, 1, 1, 1, 1
1, -1, 1, -1, 7
1, 1, 1, 0, -5
1, -1, 1, 0, -5
but I get
1 0 1 0 0
0 1 0 0 0
0 0 0 1 0
0 0 0 0 1
I could use some help,
Thank you