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: white (taw933) HW06 benzvi (55600) 1 This printout should have 16 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 (0) when f ( x ) = (1 6 x ) 4 . Correct answer: 24. Explanation: Using the chain rule and the fact that ( x ) = x 1 , we obtain f ( x ) = 24 (1 6 x ) 5 . At x = 0, therefore, f (0) = 24 . 002 10.0 points Find the derivative of f when f ( x ) = sin(cos x ) . 1. f ( x ) = cos x sin(sin x ) 2. f ( x ) = cos x sin(cos x ) 3. f ( x ) = sin x cos(sin x ) 4. f ( x ) = cos x sin(cos x ) 5. f ( x ) = sin x cos(cos x ) 6. f ( x ) = sin x cos(cos x ) correct Explanation: Using the Chain Rule we see that f ( x ) = parenleftBig cos(cos x ) parenrightBig ( sin x ) = sin x cos(cos x ) . 003 10.0 points Find the derivative of f when f ( x ) = parenleftBig 2 x 7 / 2 3 x 7 / 2 parenrightBig 2 . 1. f ( x ) = 7 parenleftbigg 4 x 14 9 x 8 parenrightbigg correct 2. f ( x ) = 8 parenleftbigg 4 + 3 x 14 x 7 parenrightbigg 3. f ( x ) = 7 parenleftbigg 2 x 7 + 3 x 7 parenrightbigg 4. f ( x ) = 8 parenleftbigg 4 3 x 14 x 7 parenrightbigg 5. f ( x ) = 8 parenleftbigg 4 x 14 + 9 x 8 parenrightbigg 6. f ( x ) = 7 parenleftbigg 2 x 14 3 x 7 parenrightbigg Explanation: After expansion, parenleftBig 2 x 7 / 2 3 x 7 / 2 parenrightBig 2 = 4 x 7 12 + 9 x 7 Thus f ( x ) = 28 x 6 63 x 8 = 28 x 6 63 x 8 . Consequently, f ( x ) = 7 parenleftbigg 4 x 6 9 x 8 parenrightbigg = 7 parenleftbigg 4 x 14 9 x 8 parenrightbigg . 004 10.0 points Find the x and yintercepts of the tangent line to the graph of y = ( 3 x + 5 ) 1 / 3 at the point (1 , 2). white (taw933) HW06 benzvi (55600) 2 1. xintercept = 5 3 , yintercept = 5 12 2. xintercept = 20 3 , yintercept = 11 6 3. xintercept = 6 , yintercept = 3 2 4. xintercept = 7 , yintercept = 7 4 correct 5. xintercept = 21 4 , yintercept = 7 4 Explanation: By the power rule, dy dx = ( 3 x + 5 ) 1 / 3 1 ....
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.
 Spring '08
 schultz
 Derivative, Differential Calculus

Click to edit the document details