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Section 3.4-solutions-1 - troyer(lmt836 Section 3.4...

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troyer (lmt836) – Section 3.4 – isaacson – (55826) 1 This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Find the derivative of g when g ( x ) = x 3 cos x. 1. g ( x ) = x 2 (3 cos x - x sin x ) correct 2. g ( x ) = x 2 (3 cos x + x sin x ) 3. g ( x ) = x 2 (3 sin x + x cos 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 3 (2 cos x - sin x ) 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 ) . 002 10.0points Find the x -intercept of the tangent line to the graph of f ( x ) = 4 x + 3 cos x at the point (0 , f (0)). 1. x -intercept = 4 3 2. x -intercept = 3 4 3. x -intercept = - 4 7 4. x -intercept = 3 7 5. x -intercept = - 4 3 6. x -intercept = - 3 4 correct Explanation: When f ( x ) = 4 x + 3 cos x, then f ( x ) = 4 - 3 sin x. Thus at x = 0, f (0) = 3 , f (0) = 4 . So by the Point-Slope formula, an equation for the tangent line at (0 , f (0)) is y - 3 = 4( x - 0) , which after rearranging become y = 4 x + 3 .
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