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: Garcia, Ilse Homework 6 Due: Oct 2 2007, 3:00 am Inst: Fonken 1 This printout should have 20 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 Determine the derivative of f when f ( x ) = 4 5 2 / 3 . 1. f ( x ) = 2 3 4 5  1 / 3 2. f ( x ) does not exist 3. f ( x ) = 8 15 x 1 / 3 4. f ( x ) = 0 correct 5. f ( x ) = 4 5 x 1 / 3 Explanation: The derivative of any constant function is zero. Consequently, f ( x ) = 0 . keywords: derivative, constant function 002 (part 1 of 1) 10 points Find the xcoordinates of all the points on the graph of f at which the tangent line is horizontal when f ( x ) = x 3 + x 2 x + 5 . 1. xcoord = 1 3 2. xcoord = 1 3. xcoords = 1 3 , 1 4. xcoord = 1 5. xcoord = 1 3 6. xcoords = 1 3 , 1 correct Explanation: The tangent line will be horizontal at P ( x ,f ( x )) when f ( x ) = 0 . Now f ( x ) = 3 x 2 + 2 x 1 = (3 x 1)( x + 1) . Consequently, x = 1 3 , 1 . keywords: horizontal tangent line, extrema, polynomials, derivative 003 (part 1 of 1) 10 points Differentiate the function f ( x ) = 7 x 8 1. df dx = 8 7 x 7 2. df dx = 8 7 x 9 correct 3. df dx = 7 8 x 7 4. df dx = 8 7 x 9 5. df dx = 9 7 x 9 Explanation: f ( x ) = 7 x 8 = 7 x 8 f ( x ) = 8 7 x 9 = 8 7 x 9 Garcia, Ilse Homework 6 Due: Oct 2 2007, 3:00 am Inst: Fonken 2 keywords: derivative, rational function 004 (part 1 of 1) 10 points Find the derivative of f ( x ) = ( x 3 + 1)(1 2 x 2 ) . 1. f ( x ) = 3 x 2 4 x 10 x 3 2. f ( x ) = 3 x 3 + 4 x 2 10 x 4 3. f ( x ) = 3 x 3 4 x 2 10 x 4 4. f ( x ) = 3 x 2 + 4 x 10 x 3 5. f ( x ) = 3 x 2 4 x 10 x 4 correct Explanation: By the Product rule f ( x ) = 3 x 2 (1 2 x 2 ) 4 x ( x 3 + 1) . Thus f ( x ) = 3 x 2 4 x 10 x 4 . keywords: derivatives, product rule 005 (part 1 of 1) 10 points Find the derivative of f when f ( x ) = x (2 x + 1) . 1. f ( x ) = 6 x 1 2 x 2. f ( x ) = 4 x + 1 x x 3. f ( x ) = 6 x + 1 2 x correct 4. f ( x ) = 6 x 1 x x 5. f ( x ) = 4 x 1 x x 6. f ( x ) = 4 x + 1 2 x Explanation: By the Product Rule f ( x ) = 2 x + 1 2 x + 2 x. After simplification this becomes f ( x ) = 2 x + 1 + 4 x 2 x = 6 x + 1 2 x ....
View
Full
Document
This note was uploaded on 09/28/2008 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