Find a third degree polynomial P(x)

Question

Find a third degree polynomial P(x)

Such that...

P(1)=7

P'(2)=-10

P''(5)=-30

and P'''(3)=-12

Answer 1

Then y''''=-12

Y''= -12x+c

-30= -60+c

C=30

So y''= -12x+30

Y'= -6x^2 +30x +c

-10 = -24+60+c

C=-46

Y'=-6x^2 +30x -46

Y= -3x^3 +15x^2-46x+c

7=-3+15-46+c

C=41

Y=-3x^3 +15x^2-46x+41