review 1 ans - Lescure Etienne – Review 1 – Due 10:00...

Info iconThis preview shows pages 1–4. 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

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: Lescure, Etienne – Review 1 – Due: Dec 10 2007, 10:00 pm – Inst: Diane Radin 1 This print-out should have 20 questions. Multiple-choice 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 Find the derivative of g when g ( x ) = x 4 cos x . 1. g ( x ) = x 4 (3 cos x- sin x ) 2. g ( x ) = x 3 (4 cos x- x sin x ) correct 3. g ( x ) = x 3 (4 sin x- x cos x ) 4. g ( x ) = x 3 (4 cos x + x sin x ) 5. g ( x ) = x 4 (3 sin x- cos x ) 6. g ( x ) = x 3 (4 sin x + x cos x ) Explanation: By the Product rule, g ( x ) = x 4 (- sin x ) + (cos x ) · 4 x 3 . Consequently, g ( x ) = x 3 (4 cos x- x sin x ) . keywords: derivative, product rule, trigono- metric function 002 (part 1 of 1) 10 points Find the derivative of the function f ( x ) = 3- 2 x x . 1. f ( x ) = 6- 2 x x 2 2. f ( x ) = 6- 2 x x 3 3. f ( x ) = 4- 3 x x 3 correct 4. f ( x ) = 4- 3 x x 2 5. f ( x ) = 4 + 3 x x 3 Explanation: After simplification, 3- 2 x x = 3 x- 2 x 2 . Thus by the Quotient Rule, f ( x ) = 3 x 2- 2 x (3 x- 2) x 4 . Consequently, f ( x ) = 4- 3 x x 3 . keywords: derivatives, quotient rule 003 (part 1 of 1) 10 points Find the derivative of f when f ( x ) = sin x 1- 4 cos x . 1. f ( x ) = cos x- 4 (1- 4 cos x ) 2 correct 2. f ( x ) = sin x- 4 1- 4 cos x 3. f ( x ) = cos x + 4 1- 4 cos x 4. f ( x ) = cos x + 4 (1- 4 cos x ) 2 5. f ( x ) = sin x- 4 cos 2 x (1- 4 cos x ) 2 Lescure, Etienne – Review 1 – Due: Dec 10 2007, 10:00 pm – Inst: Diane Radin 2 6. f ( x ) = cos x- 4 sin 2 x (1- 4 cos x ) 2 Explanation: By the Quotient Rule, f ( x ) = cos x (1- 4 cos x )- 4 sin x sin x (1- 4 cos x ) 2 = cos x- 4 (cos 2 x + sin 2 x ) (1- 4 cos x ) 2 . But cos 2 x + sin 2 x = 1, so f ( x ) = cos x- 4 (1- 4 cos x ) 2 . keywords: derivative, trigonometric function, quotient rule 004 (part 1 of 1) 10 points There is one point in the first quadrant at which the tangent line to the graph of y = 5 + x + x 2- x 3 is horizontal. Find the y-coordinate of this point. 1. y = 6 correct 2. y = 8 3. y = 7 4. y = 9 5. y = 5 Explanation: The tangent line to the graph will be hori- zontal when dy dx = 1 + 2 x- 3 x 2 = (3 x + 1)(1- x ) = 0 . The only solution of this for which x > 0 oc- curs at x = 1. But at x = 1 the corresponding value of y is y = 6. Since this value of y is positive, the only point in the first quadrant at which the tangent line is horizontal is the point P = (1 , 6) . keywords: horizontal tangent line, derivative, extrema, polynomial 005 (part 1 of 1) 10 points If f is a function defined on (- 2 , 2) whose graph is 1 2- 1- 2 1 2- 1- 2 which of the following is the graph of its derivative f ? 1. 1 2- 1- 2 1 2- 1- 2 Lescure, Etienne – Review 1 – Due: Dec 10 2007, 10:00 pm – Inst: Diane Radin 3 2....
View Full Document

This note was uploaded on 03/18/2008 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas.

Page1 / 11

review 1 ans - Lescure Etienne – Review 1 – Due 10:00...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online