Answer:
60
Step-by-step explanation:
The given function is:
[tex]h(t)=-16t^2+120t+6[/tex]
The average rate of change of h(t) from t=a to t=b is given by:
[tex]\frac{h(b)-h(a)}{b-a}[/tex]
We can rewrite this function as: [tex]h(t)=-16(t-3.75)^2+231[/tex]
The maximum height of the rocket is 231 and it occurs at t=3.75
[tex]\implies h(3.75)=231[/tex]
The initial launch occurs at: t=0
and [tex]h(0)=-16(0)^2+120(0)+6=6[/tex]
The average rate of change from the initial launch to the maximum height is
[tex]\frac{h(3.75)-h(0)}{3.75-0}=\frac{231-6}{3.75-0} =60[/tex]
