1. Determine whether Rolle's Theorem can be applied tof on the closed interval
[a, b].
(Select all that apply.)
Yes,Rolle's Theorem can be applied.No, because f isnot continuous on the closed interval [a,b].No, because f isnot differentiable in the open interval (a,b).No, becausef(a) ≠f(b).
If Rolle's Theorem can be applied, find all values ofc in the open interval
(a, b)
such that
f '(c)= 0.
(Enter your answers as a comma-separated list. If Rolle's Theoremcannot be applied, enter NA.)
2. The height of an object t seconds after it is dropped from a height of 230meters is
s(t)= −4.9t2 + 230.
(a) Find the average velocity of the object during the first 6seconds.
m/s
(b) Use the Mean Value Theorem to verify that at some time duringthe first 6 seconds of fall, the instantaneous velocity equals theaverage velocity. Find that time.
s
