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I am doing a lab for my calculus class and doing problems such as these were not discussed, needless to say I am a bit lost. If anyone could explain what to do or where to start I would appreciate it. I do not expect someone to flat out answer and prefer otherwise, I need to learn how to do it! Thank you so much in advance!

Under the influence of various forces, the altitude $h(t)$ of a rocket from its moment of launch until its fall to Earth is given by the formula $h(t)=-t^4+8t^3-3t^2+10t+375$, with $h$ in feet above sea level and $t$ in seconds.

(a) From what altitude is the rocket launched? (b) When does the rocket fall into the ocean? (c) What is the rocket's maximum altitude? (d) What is the rocket's maximum upward velocity? (e) What is the rocket's maximum downward velocity? (f) What is the rocket's maximum upward acceleration? (g) What is the rocket's maximum downward acceleration?

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Hints a)The launch is $t=0$. b)The ocean is when $h=0$ c)When you see maximum, that should make you think take the derivative, set to zero. d,e)Velocity is $\frac {dh}{dt}$, so take its derivative to find the maximum. f,g)Acceleration is $\frac {d^2h}{dt^2}$

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