Question

find the polynomial: \[p(x)=c_3x^3+c_2x^2+c_1x^1+c_0\]
such that: p(-1) = -5
p( 2) =13
p'(-1) = 12
p' ( 2) = 9

Answer 1

\[p'(x)=3c_3x^2+2c_2x+c_1\]
\[p'(-1)=3c_3-2c_2+c_1=12\]
\[p'(2)=12c_3+8c_2+c_1=9\]
\[p(-1)=-c_3+c_2-c_1+c_0=-5\]
\[p(2)=8c_3+4c_2+2c_1+c_0=9\]

Answer 2

You have 4 equations from the info given

Answer 3

I think putting this in matrix form will be fancy but easier

Answer 4

yep, rref the coeff matrix with the right sides

Answer 5

when I first tried it I kept switching numbers about and not getting a good bead on it; so I ended up do a similar but longer route combining a few methods :)