Here is a review for your upcoming test. The test covers sections 3.4 through 4.6. I will not collect this. Do what you want with it. This review will give you a good indication of what you will be expected to know for the test.
Here is a list of things that you must know and understand:
Reminders: During the exam, SHOW ALL YOUR WORK and JUSTIFY YOUR ANSWERS when necessary. Also, be organized and neat!
Answer each of the following questions.
16. Given , show that f satisfies the hypotheses of the Mean Value Theorem on the interval , and then find all c in the interval that satisfy the conclusion of the Mean Value Theorem.
17. A point moves along the curve in such a way that the y-value is decreasing at a rate of 2 meters per second. At what rate is x changing when ?
18. An interstellar nugget is circling the planet Earth a mile from its surface in a clockwise direction. An observer is standing at a fixed location watching the nugget with his nuggetscope. If the nugget is traveling at a rate of 200 mph, then what is the rate of change in the angle of elevation of the nuggetscope when the angle is ? For this problem, assume the surface of the Earth is “locally” flat (not round). For this problem, assume that the observer is standing facing the nugget with the nugget approaching.
19. Determine the intervals where the following functions are increasing, decreasing, concave up, and concave down.
20. Find the coordinates of the local maximum, local minimum, and inflection points of the following functions.
21. Sketch the graph of by finding x-intercepts, y-intercept, intervals of increase and decrease, coordinates of turning points (local max/min), intervals of concavity, coordinates of inflection points.
22. The position function for a nugget is given by where t is measured in seconds and is measured in feet. Find the acceleration of the nugget when .
23. Find the linear approximation for at .
24. Approximate the value of using a linear approximation.
25. Find for each of the following.