Answer: [tex]636\ ft[/tex]
Step-by-step explanation:
Given
The height of the rocket is given by
[tex]Y=-16x^2+190x+72[/tex]
Maximum height is given by the derivative of y and putting it to 0
[tex]\Rightarrow \dfrac{dy}{dx}=-32x+190\\\\\Rightarrow -32x+190=0\\\Rightarrow x=\dfrac{190}{32}\\\Rightarrow x=5.93\ s[/tex]
Put the value of x in y
[tex]\Rightarrow y=-16(5.93)^2+190(5.93)+72\\\Rightarrow y=-562.638+1126.7+72\\\Rightarrow y=636.06\ ft[/tex]
