Answer with Step-by-step explanation:
We are given that
Height of ball after t seconds is given by
[tex]s(t)=-4t^2+20t+2[/tex]
a.Substitute the value of t=1
[tex]s(1)=-4(1)+20(1)+2=-4+20+2=18 ft[/tex]
b.Differentiate w.r.t x
[tex]s'(t)=-8t+20[/tex]
[tex]s'(t)=0[/tex]
[tex]-8t+20=0[/tex]
[tex]8t=20[/tex]
[tex]t=\frac{20}{8}=2.5[/tex]
Again differentiate w.r.t t
[tex]s''(t)=-8<0[/tex]
Hence, the height is maximum at t=2.5 s
[tex]s(2.5)=-4(2.5)^2+20(2.5)+2=27[/tex]
Maximum height of the baseball=27 ft
