This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: obiahu (vo879) HW05 Schultz (56395) 1 This printout should have 21 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find the value of f (4) when f ( x ) = 5 3 x 3 / 2 + 6 x 1 / 2 . 1. f (4) = 6 2. f (4) = 7 3. f (4) = 11 2 4. f (4) = 5 5. f (4) = 13 2 correct Explanation: Since d dx x r = rx r 1 , we see that f ( x ) = 5 2 x 1 / 2 + 3 x 1 / 2 . At x = 4, therefore, f (4) = 13 2 . 002 10.0 points Find the xcoordinate of all points on the graph of f ( x ) = x 3 2 x 2 4 x + 4 at which the tangent line is horizontal. 1. xcoord = 2 3 2. xcoords = 2 3 , 2 correct 3. xcoord = 2 4. xcoord = 2 3 5. xcoords = 2 3 , 2 6. xcoord = 2 Explanation: The tangent line will be horizontal at P ( x , f ( x )) when f ( x ) = 0 . Now f ( x ) = 3 x 2 4 x 4 = (3 x + 2)( x 2) . Consequently, x = 2 3 , 2 . 003 10.0 points Find the derivative of f when f ( x ) = x 7 2 + 2 x 3 2 1 x . 1. f ( x ) = 7 x 9 2 6 x 1 2 1 x 2 2. f ( x ) = 5 x 9 2 + 6 x 3 2 + 2 2 x 2 3. f ( x ) = 5 x 7 2 2 x 3 2 + 1 2 x 2 4. f ( x ) = 7 x 7 2 2 x 1 2 2 2 x 2 5. f ( x ) = 7 x 9 2 6 x 1 2 + 2 2 x 2 correct Explanation: Since d dx x r = rx r 1 obiahu (vo879) HW05 Schultz (56395) 2 holds for all real numbers r , we see that f ( x ) = 7 2 x 5 2 3 x 5 2 + 1 x 2 . To simplify this expression we bring the right hand side to a common denominator so that f ( x ) = 7 x 9 2 6 x 1 2 + 2 2 x 2 . 004 10.0 points Find the derivative of g ( x ) = parenleftbigg x + 2 x + 1 parenrightbigg (2 x 9) . 1. g ( x ) = 2 x 2 4 x 13 x + 1 2. g ( x ) = x 2 4 x + 13 x + 1 3. g ( x ) = 2 x 2 + 4 x + 13 ( x + 1) 2 correct 4. g ( x ) = 2 x 2 + 4 x + 13 x + 1 5. g ( x ) = 2 x 2 4 x 13 ( x + 1) 2 6. g ( x ) = x 2 + 4 x 13 ( x + 1) 2 Explanation: By the Quotient and Product Rules we see that g ( x ) = 2 braceleftbigg x + 2 x + 1 bracerightbigg + (2 x 9) braceleftbigg ( x + 1) ( x + 2) ( x + 1) 2 bracerightbigg = 2 braceleftbigg x + 2 x + 1 bracerightbigg + braceleftbigg 2 x 9 ( x + 1) 2 bracerightbigg = 2( x + 2)( x + 1) + (2 x 9) ( x + 1) 2 . But 2( x + 2)( x + 1) (2 x 9) = 2 x 2 + 4 x + 13 ....
View
Full
Document
This note was uploaded on 09/06/2010 for the course M 32795 taught by Professor Schultz during the Spring '10 term at University of Texas at Austin.
 Spring '10
 schultz

Click to edit the document details