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Unformatted text preview: Math 16A: Practice problems Final Exam
The final will have two parts. The first part will be like a third midterm, and will cover sections 2.7, 2.8, 3.1-3.4, 3.7, and 3.8. The second part will cover material from Midterm 1 and Midterm 2. These are practice problems for the first part of the final. 1. Find dy dx at the point (2, -1), if x2 y + y 2 x = -2. 2. The rate of change of a circle is increasing at a rate of 3 inches per minute. Find the rates of change of the area when (a) r = 5 inches and (b) r = 10 inches. (Hint: The area of a circle of radius r is r2 .) 3. All edges of a cube are expanding at a rate of 3 cubic inches per second. How fast is the surface area changing when each edge is (a) 1 inch and (b) 10 inches? 4. Find all relative extrema of the function f (x) = x3 - 2x2 - 3x.
x 5. Consider the function f (x) = x+2 . Find the intervals on which f (x) is increasing and decreasing. Also find the intervals on which f (x) is concave up and concave down.
2 6. Find the absolute maximum of f (x) = 5 - 2x2 on the interval [0, 3]. 7. Find the length and width of a rectangle that has perimeter 10 meters and a maximum area. 8. Sketch the graph of f (x) = x2 +1 . Include the interx -2 cepts, relative extrema, points of inflection, and asymptotes. Also, state the domain of the function.
2 9. Let f (x) = x3 . Let x = 1 and dx = x = .1. Find dy and y. 10. The combined perimeter of a circle and a square is 16. Find the dimensions of the circle and the square that produce a minimum total area. 2 ...
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