Answer: 245 feet
Step-by-step explanation:
Given: The height of the rocket after t seconds is represented by the formula:
[tex]h=70t-5t^2[/tex]
[tex]\dfrac{dh}{dt}=70-10t[/tex] [Differentiate both sides w.r.t. t]
Put
[tex]\dfrac{dh}{dt}=0\\\\\Rightarrow\ 70-10t=0\\\\\Rightarrow\ t=\dfrac{70}{10}=7[/tex]
Also, [tex]\dfrac{d^2h}{dt^2}=-10<0[/tex] i.e. height is maximum at t=7.
Maximum height = [tex]h=70(7)-5(7)^2 = 490 - 245= 245\text{ feet}[/tex]
Hence, the maximum height the rocket reaches = 245 feet.
