Math 180
Extra Credit Test 2
Due: Beginning of class Tuesday, November 10 NO EXCEPTIONS! This is BONUS work!
For each problem that is completely correct, one point will be added to either Test 2 or Test 3. All bonus points must be added to either Test 2 or Test 3. Keep in mind that the maximum score assigned on any single exam for my classes is 105. Work must be neat and organized and shown on this sheet in the spaces provided below. Any work submitted not meeting this criteria will not be graded.
For the following functions, find the derivative. Show the derivative in its most simplified form. Show work and answers on this sheet.
1. a) b)
2. 3.
4. Find the equation of the tangent line to the graph of at the point
5. Find the derivative: 6. Find the 2nd derivative:
7. Find dy/dx:
8. A ball is tossed upward from a height of 5 feet with an initial velocity of 80 ft/s.
a) Find the position, velocity and acceleration functions for this scenario.
b) How fast is the ball traveling at t = 3 seconds?
c) At what time does the ball reach its maximum height? And what is that
maximum height?
9. A balloon is 200 ft off the ground and rising vertically at a rate of 15 ft/sec. An automobile passes beneath it traveling along a straight road at a constant rate of 45mph (66 ft/sec). How fast is the distance between them changing one second later?
10. Find all relative extrema for
11. Verify that the function satisfies Rolle’s Theorem on the interval and find all values x = c that are guaranteed by the theorem.
12. Verify that the function satisfies the Mean Value Theorem on the interval [1, 3] and then find all numbers x = c such that .
13. Determine where the function is increasing or decreasing.
14. Find the absolute extrema of on [-4, 5]
15. Determine the concavity for on .