the avrage velocity of p(t)=4.5t^2-15t+180 over[1,5]

A group of researchers found that people prefer YouTube videos that aren't too long, but not too short either. Suppose these researchers determined that the ratings people gave to a video could be approximated byR(t)=20t/t^2 + 100 where t is the length of the video in minutes and R(t) is its rating. What length of video (in minutes) will get the highest rating?

h(t)= -0.2t^4 + 4t^3 - 24t^2 + 48t Describe what the end behavior of this function is and the reason for this behavior.

f(x) = t^2(t - 7)^1/3.   Find all critiacal points and all relative maxima

Suppose the cost incurred in operating a cruise ship per hour is a+bv^33 dollars, where aand b are positive constants and v is the ship’s speed in miles per hour. At what speedshould the ship be operated between two ports (located d miles apart) to minimize thecost?

Find the relative maxima and minima, if any, of h(t)=3-t^2/3 without using a graph.

* /Q9 2 cosh(lnx) =