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HW06-solutions

# HW06-solutions - white(taw933 HW06 ben-zvi(55600 This...

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white (taw933) – HW06 – ben-zvi – (55600) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Find the value of f (0) when f ( x ) = (1 - 6 x ) 4 . Correct answer: 24. Explanation: Using the chain rule and the fact that ( x α ) = α x α 1 , we obtain f ( x ) = 24 (1 - 6 x ) 5 . At x = 0, therefore, f (0) = 24 . 002 10.0points Find the derivative of f when f ( x ) = sin(cos x ) . 1. f ( x ) = cos x sin(sin x ) 2. f ( x ) = cos x sin(cos x ) 3. f ( x ) = - sin x cos(sin x ) 4. f ( x ) = - cos x sin(cos x ) 5. f ( x ) = sin x cos(cos x ) 6. f ( x ) = - sin x cos(cos x ) correct Explanation: Using the Chain Rule we see that f ( x ) = parenleftBig cos(cos x ) parenrightBig ( - sin x ) = - sin x cos(cos x ) . 003 10.0points Find the derivative of f when f ( x ) = parenleftBig 2 x 7 / 2 - 3 x 7 / 2 parenrightBig 2 . 1. f ( x ) = 7 parenleftbigg 4 x 14 - 9 x 8 parenrightbigg correct 2. f ( x ) = 8 parenleftbigg 4 + 3 x 14 x 7 parenrightbigg 3. f ( x ) = 7 parenleftbigg 2 x 7 + 3 x 7 parenrightbigg 4. f ( x ) = 8 parenleftbigg 4 - 3 x 14 x 7 parenrightbigg 5. f ( x ) = 8 parenleftbigg 4 x 14 + 9 x 8 parenrightbigg 6. f ( x ) = 7 parenleftbigg 2 x 14 - 3 x 7 parenrightbigg Explanation: After expansion, parenleftBig 2 x 7 / 2 - 3 x 7 / 2 parenrightBig 2 = 4 x 7 - 12 + 9 x 7 Thus f ( x ) = 28 x 6 - 63 x 8 = 28 x 6 - 63 x 8 . Consequently, f ( x ) = 7 parenleftbigg 4 x 6 - 9 x 8 parenrightbigg = 7 parenleftbigg 4 x 14 - 9 x 8 parenrightbigg . 004 10.0points Find the x - and y -intercepts of the tangent line to the graph of y = ( 3 x + 5 ) 1 / 3 at the point (1 , 2).

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white (taw933) – HW06 – ben-zvi – (55600) 2 1. x -intercept = - 5 3 , y -intercept = 5 12 2. x -intercept = - 20 3 , y -intercept = 11 6 3. x -intercept = - 6 , y -intercept = 3 2 4. x -intercept = - 7 , y -intercept = 7 4 correct 5. x -intercept = - 21 4 , y -intercept = 7 4 Explanation: By the power rule, dy dx = ( 3 x + 5 ) 1 / 3 1 . Consequently, the slope of the tangent line at (1 , 2) is given by dy dx vextendsingle vextendsingle vextendsingle x =1 = 3 4(3) , so by the point slope formula, the equation of the tangent line at (1 , 2) is y - 2 = 1 4 ( x - 1) .
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