sample test

Don't "bomb out" on the sample test!!

1) Find the average rate of change for the function f(x) = 3x² + 2x. Then find the slope of the secant line between x₁ = 1 and x₂ = 3.

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

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

a) f(x) = x³ - 3x

b) f(x) = x³ - 1

5) A trough with a rectangular cross section is to be made from a long sheet of metal 24 meters wide by turning up strips along each side. Find the amount that must be turned up to give the greatest cross section.

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.

a) Find v(t)

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?

9) A ball is hit straight upward with an initial velocity of 256 feet per second. the ball's height after time t seconds is h(t) = 256t - 16t²

a) What is the velocity function?

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?