Math16Apfinal - Math 16A Practice problems Final Exam The...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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. 1 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 ...
View Full Document

{[ snackBarMessage ]}

Page1 / 2

Math16Apfinal - Math 16A Practice problems Final Exam The...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online