2artrooms
Calculators
General
Algebra
Geometry
Coordinate-geometry
Statistics
Calculus
Qna
Math
2artrooms
2artrooms
Home
General
Algebra
Geometry
Coordinate-geometry
Statistics
Calculus
Qna
Math
MATH SOLVE
Home
General
Create a table to find the third differences for the polynomial s^3 − s^2 +s for integer values of s...
4 months ago
Q:
Create a table to find the third differences for the polynomial s^3 − s^2 +s for integer values of ss from −3 to 3.
Accepted Solution
A:
Step-by-step explanation:[tex]f(s)=s^3-s^2[/tex]at s = -3[tex]f(-3)=-3^3-(-3)^2=18[/tex]at s = -2[tex]f(-2)=-2^3-(-2)^2\\\Rightarrow f(-2)=-12[/tex]at s = -1[tex]f(-1)=-1^3-(-1)^2\\\Rightarrow f(-1)=-2[/tex]at s = 0[tex]f(0)=0^3-0^2\\\Rightarrow f(0)=0[/tex]at s = 1[tex]f(1)=1^3-1^2\\\Rightarrow f(1)=0[/tex]at s = 2[tex]f(2)=2^3-2^2\\\Rightarrow f(2)=4[/tex]at s = 3[tex]f(3)=3^3-3^2\\\Rightarrow f(3)=18[/tex]First difference[tex]f(-2')=f(-2)-f(-3)=-12-18=-30[/tex][tex]f(-1')=f(-1)-f(-2')=-2--12=10[/tex][tex]f(0')=f(0)-f(-1)=0--2=2[/tex][tex]f(1')=f(1)-f(0)=0-0=0[/tex][tex]f(2')=f(2)-f(1)=4-0=4[/tex][tex]f(3')=f(3)-f(2)=18-4=14[/tex]Second difference[tex]f(-1'')=f(-1')-f(-2')=10--30=40[/tex][tex]f(0'')=f(0')-f(-1')=-8-40=-48[/tex][tex]f(1'')=f(1')-f(0')=-2--8=6[/tex][tex]f(2'')=f(2')-f(1')=14-4=10[/tex]Third difference[tex]f(0'')-f(-1'')=-8-40=48[/tex][tex]f(1'')-f(0'')=-2--8=6[/tex][tex]f(2'')-f(1'')=4--2=6[/tex][tex]f(2'')-f(1'')=10-4=6[/tex]18 -12 -2 0 0 4 18 -30 10 2 0 4 14 40 -8 -2 4 10 -48 6 6 6