HW05-solutions - white (taw933) HW05 ben-zvi (55600) 1 This...

Info iconThis preview shows pages 1–3. 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 DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: white (taw933) HW05 ben-zvi (55600) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find the x-coordinates of all the points on the graph of f ( x ) = 2 x 3 + 2 x 2 2 x + 4 at which the tangent line is horizontal. 1. x-coord = 1 3 , 1 2. x-coord = 1 3 3. x-coords = 1 3 , 1 4. x-coord = 1 3 5. x-coords = 1 , 1 3 correct 6. x-coord = 1 Explanation: The tangent line will be horizontal at P ( x , f ( x )) when f ( x ) = 0 . Now f ( x ) = 6 x 2 + 4 x 2 = 2(3 x 1)( x + 1) . Consequently, x = 1 , 1 3 . 002 10.0 points Find the value of f (1) when f ( x ) = 9 x 1 6 + 8 x 1 6 + 8 . Correct answer: 0 . 166667. Explanation: Since ( x r ) = r x r 1 holds for all real numbers r , we see that f ( x ) = 3 2 x 5 6 4 3 x 7 6 . Hence f (1) = 1 6 . 003 10.0 points Find the derivative of g ( x ) = parenleftbigg x + 3 x + 2 parenrightbigg (2 x 9) . 1. g ( x ) = x 2 8 x + 21 x + 2 2. g ( x ) = 2 x 2 8 x 21 ( x + 2) 2 3. g ( x ) = x 2 + 8 x 21 ( x + 2) 2 4. g ( x ) = 2 x 2 + 8 x + 21 x + 2 5. g ( x ) = 2 x 2 + 8 x + 21 ( x + 2) 2 correct 6. g ( x ) = 2 x 2 8 x 21 x + 2 Explanation: By the Quotient and Product Rules we see that g ( x ) = 2 braceleftbigg x + 3 x + 2 bracerightbigg + (2 x 9) braceleftbigg ( x + 2) ( x + 3) ( x + 2) 2 bracerightbigg = 2 braceleftbigg x + 3 x + 2 bracerightbigg + braceleftbigg 2 x 9 ( x + 2) 2 bracerightbigg = 2( x + 3)( x + 2) + (2 x 9) ( x + 2) 2 . white (taw933) HW05 ben-zvi (55600) 2 But 2( x + 3)( x + 2) (2 x 9) = 2 x 2 + 8 x + 21 . Consequently g ( x ) = 2 x 2 + 8 x + 21 ( x + 2) 2 . 004 10.0 points Find the derivative of f when f ( x ) = 4 x 3 + 3 x 2 + 4 . 1. f ( x ) = 6 parenleftBig 2 x 5 + 1 x 3 parenrightBig 2. f ( x ) = 6 parenleftBig 2 x 5 1 x 3 parenrightBig correct 3. f ( x ) = 2 parenleftBig 2 x 4 + 1 x 2 parenrightBig 4. f ( x ) = 6 parenleftBig 1 2 x 5 x 3 parenrightBig 5. f ( x ) = 2 parenleftBig 2 x 4 1 x 2 parenrightBig 6. f ( x ) = 2 parenleftBig 1 2 x 5 x 3 parenrightBig 7. none of the other answers Explanation: Since d dx ( x r ) = rx r 1 holds for all r , we see that f ( x ) = 12 x 2 6 x 3 . Consequently, f ( x ) = 6 parenleftBig 2 x 5 1 x 3 parenrightBig . keywords: derivatives, negative powers 005 10.0 points Find the derivative of f when f ( x ) = x x + 1 x ....
View Full Document

This note was uploaded on 12/05/2011 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas at Austin.

Page1 / 9

HW05-solutions - white (taw933) HW05 ben-zvi (55600) 1 This...

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