linear equation system, determinant and matrix

[soniettalipa]

find the fourth degree polynomial f (х)with real coefficients, for which f (1)=-3 ,f '(1)=-3 , f "(1)=12, f'"'(1)=42, f(-1)=3.

 

[Romsek]

i) write down the expression of a 4th degree polynomial using for example a, b, c, d, e as the various coefficients
ii) use the equations given, differentiating if necessary, to set up a system of 5 equations in a through e.
iii) use whatever method you like, or are instructed to, to solve these equations.
iv) write your polynomial using the coefficients just solved for
v) bask in glory

 

[Harry_the_cat]

You can'd do step (v) without some work!