Please Use Difference Quotient Method, DO NOT USE DERIVIATIVE. Communication:

A pilot who is flying at an altitude of $10000$ feet is forced to eject from his airplane. The path that his ejection seat takes is modeled by the equation, $h(t)=-16t^2+90t+10000,$ where $h(t)$ is his altitude in feet and $t$ is the time since his ejection in seconds. Estimate at what time, t $,$ the pilot is at a maximum altitude. Explain how the maximum altitude is related to the slope of the tangent line at certain points.

$q,$

$f(0+h)-f(0)$

$=-16(0+5{)}^2+70(0+h)+10000-10000$