Exam 2-solutions

Exam 2-solutions - Version 028 Exam 2 Helleloid(58250 1...

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: Version 028 Exam 2 Helleloid (58250) 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 derivative of f when f ( x ) = 4 x cos6 x . 1. f ( x ) = 4 cos 4 x- 4 x sin 6 x 2. f ( x ) = 4 cos 6 x- 24 x sin6 x correct 3. f ( x ) = 4 cos 6 x + 24 x sin4 x 4. f ( x ) = 24 cos 6 x- 4 x sin6 x 5. f ( x ) = 24 cos 6 x + 6 x sin6 x Explanation: Using the formulas for the derivatives of sine and cosine together with the Chain Rule we see that f ( x ) = (4 x ) cos 6 x + 4 x (cos 6 x ) = 4 cos 6 x- 24 x sin6 x . 002 10.0 points Determine the derivative of f ( x ) = x x- 1 . 1. f ( x ) = 2 + 3 x 2 x- 1 2. f ( x ) = 3 x- 2 2 x- 1 correct 3. f ( x ) = 2- 3 x 2 x- 1 4. f ( x ) = 2- 3 x x- 1 5. f ( x ) = 3 x- 2 x- 1 6. f ( x ) = 2 + 3 x x- 1 Explanation: By the Product and Chain Rules, f ( x ) = x- 1+ x 2 x- 1 = 2( x- 1) + x 2 x- 1 . Consequently, f ( x ) = 3 x- 2 2 x- 1 . keywords: 003 10.0 points Find the second derivative of f when f ( x ) = cos 2 x- 3 sin 2 x . 1. f ( x ) =- 5 cos2 x 2. f ( x ) =- 10 sin2 x 3. f ( x ) =- 10 cos2 x correct 4. f ( x ) =- 5 sin2 x 5. f ( x ) = 5 cos2 x 6. f ( x ) = 10 cos2 x Explanation: Differentiating once we see that f ( x ) =- 2 sin 2 x- 6 sin x cos x . Now 2 sin x cos x = sin 2 x , so f ( x ) =- 5 sin 2 x . Consequently, by differentiating once again we obtain f ( x ) =- 10 cos 2 x . Version 028 Exam 2 Helleloid (58250) 2 keywords: second derivative, trig function 004 10.0 points Find the equation of the tangent line to the graph of y 2- xy- 15 = 0 , at the point P = (2 , 5). 1. 8 y + 5 x = 30 2. 7 y = 5 x + 25 3. 2 y = 5 x 4. 8 y = 5 x + 30 correct 5. 7 y + 5 x = 25 Explanation: Differentiating implicitly with respect to x we see that 2 y dy dx- y- x dy dx = 0 , so dy dx = y 2 y- x . At P = (2 , 5), therefore, dy dx vextendsingle vextendsingle vextendsingle P = 5 8 . Thus by the point slope formula, the equation of the tangent line at P is given by y- 5 = 5 8 ( x- 2) . Consequently, 8 y = 5 x + 30 . 005 10.0 points The cost function for Levi Strauss to pro- duce x pairs of blue jeans is C ( x ) = 4700 + 7 x- 1 50 x 2 + 3 5000 x 3 . Find the marginal cost to Levi Strauss of producing 100 pairs of blue jeans. 1. marginal cost = $22 per pair 2. marginal cost = $21 per pair correct 3. marginal cost = $25 per pair 4. marginal cost = $24 per pair 5. marginal cost = $23 per pair Explanation: By definition, the Marginal cost is the derivative, C ( x ), of the cost function C ( x )....
View Full Document

This note was uploaded on 12/04/2009 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas.

Page1 / 10

Exam 2-solutions - Version 028 Exam 2 Helleloid(58250 1...

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