Step-by-step explanation:
[tex]f(t)=36-16t^2[/tex]
at t = 0
[tex]y=36[/tex]
at t = 1
[tex]f(1)=36-16\times 1^2\\\Rightarrow f(1)=20[/tex]
at t = 2
[tex]f(2)=36-16\times 2^2\\\Rightarrow f(2)=-28[/tex]
at t = 3
[tex]f(3)=36-16\times 3^2\\\Rightarrow f(3)=-108[/tex]
at t = 4
[tex]f(4)=36-16\times 4^2\\\Rightarrow f(4)=-220[/tex]
at t = 5
[tex]f(4)=36-16\times 5^2\\\Rightarrow f(5)=-364[/tex]
First difference
[tex]f(1)'=f(1)-f(0)=20-36=-14[/tex]
[tex]f(2)'=f(2)-f(1)=-28-20=-48[/tex]
[tex]f(3)'=f(3)-f(2)=-108--28=-80[/tex]
[tex]f(4)'=f(4)-f(3)=-220--108=-112[/tex]
[tex]f(5)'=f(5)-f(4)=-364--220=-144[/tex]
Second difference
[tex]f(2)'-f(1)'=-48--14=-34[/tex]
[tex]f(3)'-f(2)'=-80--48=-32[/tex]
[tex]f(4)'-f(3)'=-112--80=-32[/tex]
[tex]f(5)'-f(4)'=-144--112=-32[/tex]
0 20 -28 -108 -220 -364
-14 -48 -80 -112 -144
-34 -32 -32 -32
