This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Granillo, Yvette – Homework 5 – Due: Sep 29 2005, 3:00 am – Inst: Edward Odell 1 This printout should have 22 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points If f is a function defined on ( 2 , 2) whose graph is 1 2 1 2 1 2 1 2 which of the following is the graph of its derivative f ? 1. 1 2 1 2 1 2 1 2 2. 1 2 1 2 1 2 1 2 3. 1 2 1 2 1 2 1 2 4. 1 2 1 2 1 2 1 2 correct 5. 1 2 1 2 1 2 1 2 6. 1 2 1 2 1 2 1 2 Explanation: Since the graph on ( 2 , 2) consists of straight lines joined at x = 1 and x = 1, the derivative of f will exist at all points in ( 2 , 2) except x = 1 and x = 1, eliminating the answer whose graph contain filled dots at x = 1 and x = 1. On the other hand, the graph of f (i) has slope 1 on ( 2 , 1), (ii) has slope 2 on ( 1 , 1), and Granillo, Yvette – Homework 5 – Due: Sep 29 2005, 3:00 am – Inst: Edward Odell 2 (iii) has slope 1 on (1 , 2). Consequently, the graph of f consists of the horizontal lines and ‘holes’ in 1 2 1 2 1 2 1 2 keywords: Stewart5e, graph, derivative, piecewise linear function 002 (part 1 of 2) 10 points Compute the lefthand derivative f ( a ) = lim h → f ( a + h ) f ( a ) h and righthand derivative f + ( a ) = lim h → + f ( a + h ) f ( a ) h of f at x = 6 when f ( x ) = 7 x, x < 6 , 1 7 x , x ≥ 6 . 1. f (6) = 1 , f + (6) = 1 2. f (6) = 1 , f + (6) = 1 correct 3. f (6) = 6 , f + (6) = 6 4. f (6) = 4 , f + (6) = 4 5. f (6) = 6 , f + (6) = 6 6. f (6) = 1 , f + (6) = 1 7. f (6) = 4 , f + (6) = 4 Explanation: Since f (6) = 1, the definition of f ( a ) and f + ( a ) ensure that f (6) = lim h → { 7 (6 + h ) } 1 h = lim h → µ h h ¶ = 1 , while f + (6) = lim h → + ‰ 1 7 (6 + h ) 1 ¾ h = lim h → + 1 (1 h ) h (1 h ) = lim h → + 1 1 h = 1 . Consequently, f (6) = 1 , f + (6) = 1 . 003 (part 2 of 2) 10 points (ii) Use your results from part (i) to deter mine if f (6) exists, and if it does, find its value. 1. f (6) does not exist correct 2. f (6) = 1 3. f (6) = 6 4. f (6) = 0 5. f (6) = 4 6. f (6) = 1 Granillo, Yvette – Homework 5 – Due: Sep 29 2005, 3:00 am – Inst: Edward Odell 3 7. f (6) = 4 Explanation: The derivative f (6) of f at x = 6 will exist if both the respective left and right hand derivatives f (6) and f + (6) exist and f (6) = f + (6). part (i) shows that these onesided derivatives exist, but are not equal. Consequently, f (6) does not exist . keywords: Stewart5e, left hand derivative, right hand derivative, derivative, piecewise defined function 004 (part 1 of 1) 10 points Find the value of f (4) when f ( x ) = 2 3 x 3 / 2 2 x 1 / 2 ....
View
Full
Document
This test prep was uploaded on 04/16/2008 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas at Austin.
 Spring '08
 schultz

Click to edit the document details