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This Question: 1 pt
A baseball is hit so that its height in feet after t seconds is s(t) = - 4t"" + 20t+2.
(a) How high is the baseball after 1 second?
(b) Find the maximum height of the baseball.​

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lublana

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

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