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

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

myininaya · Answer

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

myininaya · Answer

You have 4 equations from the info given

myininaya · Answer

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

amistre64 · Answer

yep, rref the coeff matrix with the right sides

amistre64 · Answer

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 :)

myininaya · Answer

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