Test2 - the derivative of a mysterious function named f ....

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Name 27 October 2011 Teaching Assistant Hour Test 2 Math 1501 C Andrew Instructions: 1. Closed book. 2. Show your work and explain your answers and reasoning. 3. Calculators may be used, but are by no means necessary. Pay particular attention to instruction 2. To receive credit, you must show your work. Unexplained answers, and answers not supported by the work you show, will not receive credit. 4. Express your answers in simplified form. 1. (25) Evaluate a. n n n 3 1 1 lim - + b. n n n - 2 1 lim c. π 0 2 sin cos dx x x d. The first and second derivatives of ( 29 = x dt t x F 2 2 ) sin( 2. (25) A cookie box, as shown below, has been made from a 12 inch by 12 inch square of cardboard. Find the value of x that maximizes the volume of the box, and use the second derivative test to show that you have found a local maximum.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Name Page 2 of 3 Hour Test 2 Teaching Assistant 27 October 2011 3. (25) Drawn at the left is the graph of
Background image of page 2
Background image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: the derivative of a mysterious function named f . On the right is a blank set of axes. Graph of x d f d a. On what interval(s) is f increasing? Explain your answer. b. On what interval(s) is f decreasing? Explain your answer. c. Tell me the critical point(s) of f , and tell me which are local minima and which are local maxima. Explain your answer. d. For which value(s) of x is ? 2 2 = x d x d Explain your answer. 4. (25) Sketch the region bounded by the parabola 1 2 + = x y and the line 9 2 +-= x y , and calculate the area of this region. Name Page 3 of 3 Hour Test 2 Teaching Assistant 27 October 2011 ANSWERS 1. a. 3-e b. 2-e c. 3 2 d. ) cos( 2 , ) sin( 2 2 x x x 2. 24 ) 2 ( ' ' , 2 <-= = V x 3. a. ) , 2 ( ) , ( -and b. ) 2 , ( c. By the first derivative test, there is a local maximum at 0 and a local minimum at 2. d. -1 and 1 4. The area is 36...
View Full Document

This note was uploaded on 01/16/2012 for the course MATH 1501 taught by Professor N/a during the Fall '08 term at Georgia Institute of Technology.

Page1 / 3

Test2 - the derivative of a mysterious function named f ....

This preview shows document pages 1 - 3. Sign up to view the full document.

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