2) Using the definition of the derivative, find f '(x) if f(x) = 2x2 - 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
by using the formulas and then find f '(-1).
4) Find the critical points of each function and graph each function.
b) f(x) = x3 - 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) = 16t2 - 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?