posted by Angelina .
The height of a ball t seconds after it is thrown upward from a height of 6 feet and with an initial velocity of 80 feet per second is f (t) = -16t^2 + 80t + 6.
According to Rolle's Theorem, what must be the velocity at some time in the interval (2, 3)?
& Find that time t?
I believe i need to take the 1st derivative which is -32t+80 equal to zero so t=-80/32? and for ft/sec plug in 2 for t? Anyhow i get wrong answers so need help!
You are correct on the time, but it needs to be simplified if not put into decimal form. Now you need to plug in 2 into the orignal problem and get a resultant, then plug in three to the original problem as well. If they are the same resultant then they follow rolles theorem. There are some rules to this theorem like is it a continuous function, is it differentialable? Keep those things in mind because if you go on to Calculus 2, you will see these again in integratable series.