This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Barkley, Thane Review 1 Due: Dec 11 2007, 3:00 am Inst: Louiza Fouli 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 Find the derivative of g when g ( x ) = x 3 cos x . 1. g ( x ) = x 2 (3 sin x x cos x ) 2. g ( x ) = x 3 (2 cos x sin x ) 3. g ( x ) = x 2 (3 cos x + x sin x ) 4. g ( x ) = x 3 (2 sin x cos x ) 5. g ( x ) = x 2 (3 sin x + x cos x ) 6. g ( x ) = x 2 (3 cos x x sin x ) correct Explanation: By the Product rule, g ( x ) = x 3 ( sin x ) + (cos x ) 3 x 2 . Consequently, g ( x ) = x 2 (3 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 ) = 4 3 x x . 1. f ( x ) = 8 3 x x 2 2. f ( x ) = 6 4 x x 2 3. f ( x ) = 6 + 4 x x 3 4. f ( x ) = 6 4 x x 3 correct 5. f ( x ) = 8 3 x x 3 Explanation: After simplification, 4 3 x x = 4 x 3 x 2 . Thus by the Quotient Rule, f ( x ) = 4 x 2 2 x (4 x 3) x 4 . Consequently, f ( x ) = 6 4 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 2 cos x . 1. f ( x ) = sin x 2 cos 2 x (1 2 cos x ) 2 2. f ( x ) = sin x 2 1 2 cos x 3. f ( x ) = cos x 2 (1 2 cos x ) 2 correct 4. f ( x ) = cos x + 2 1 2 cos x 5. f ( x ) = cos x + 2 (1 2 cos x ) 2 Barkley, Thane Review 1 Due: Dec 11 2007, 3:00 am Inst: Louiza Fouli 2 6. f ( x ) = cos x 2 sin 2 x (1 2 cos x ) 2 Explanation: By the Quotient Rule, f ( x ) = cos x (1 2 cos x ) 2 sin x sin x (1 2 cos x ) 2 = cos x 2 (cos 2 x + sin 2 x ) (1 2 cos x ) 2 . But cos 2 x + sin 2 x = 1, so f ( x ) = cos x 2 (1 2 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 = 4 + x + x 2 x 3 is horizontal. Find the ycoordinate of this point. 1. y = 6 2. y = 5 correct 3. y = 7 4. y = 4 5. y = 8 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 = 5. 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 , 5) . 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 Barkley, Thane Review 1 Due: Dec 11 2007, 3:00 am Inst: Louiza Fouli 3 2....
View Full
Document
 Fall '08
 schultz
 Calculus

Click to edit the document details