*2) Using the
definition
of the derivative, find f '(x) if f(x) = 2x ^{2}
- 5. Find the slope of the tangent line at x = 2, x = 0, x = -2. Tell
if
it is increasing, decreasing or zero at that point.*

*3) Find the
derivatives
by using the formulas and then find f '(-1).*

*4) Find the critical points of each function
and
graph each function.*

*b) f(x) = x ^{3}
- 1*

*6) There are 900 feet of fencing
available
to enclose a rectangular plot of ground with a fence down the middle
and
parallel to two ends. What is the maximum area which can be
enclosed?*

*7) A bus company carries 2000
passengers per
day at a rate of 20 cents per passenger. In determining a rate
hike,
the head dudes estimate that they would lose 200 passengers for every 5
cents they increase the rates. What rate should they charge to
maximize
their income?*

*8) Let s(t) = 16t ^{2}
- 128t + 8. Answer each question.*

*b) Find the velocity at t = 3, t =
4, t =
5. What does each answer mean?*

*c) Find a(t)*

*d) Find the acceleration at t = 1, t
= 3,
t = 3. What do the answers indicate?*

*b) What is the velocity at t = 6, t
= 8, t
= 10?*

*c) What is the acceleration function?*

*d) At what time does the ball hit
the ground?*

*e) What is the velocity of the ball
when it
hits the ground?*

*f) What time does it reach maximum
height?*

*g) What is the maximum height?*

* *