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Section 3.6-solutions-1 - troyer(lmt836 Section 3.6...

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troyer (lmt836) – Section 3.6 – 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 y when xy + 3 x + 4 x 2 = 1 . 1. y = - y + 3 + 4 x x 2. y = - ( y + 3 + 8 x ) 3. y = y + 3 + 8 x x 4. y = 3 + 4 x - y x 5. y = y + 3 + 4 x x 6. y = - y + 3 + 8 x x correct Explanation: Differentiating implicitly with respect to x we see that d dx ( xy + 3 x + 4 x 2 ) = d dx (1) . Thus ( xy + y ) + 3 + 8 x = 0 , and so xy = - y - 3 - 8 x . Consequently, y = - y + 3 + 8 x x . 002 10.0points If y = y ( x ) is defined implicitly by y 2 + xy + 3 = 0 , find the value of dy/dx at the point (4 , - 1). 1. dy dx vextendsingle vextendsingle vextendsingle (4 , 1) = - 1 2 2. dy dx vextendsingle vextendsingle vextendsingle (4 , 1) = - 3 2 3. dy dx vextendsingle vextendsingle vextendsingle (4 , 1) = 1 2 correct 4. dy dx vextendsingle vextendsingle vextendsingle (4 , 1) = 3 2 5. dy dx vextendsingle vextendsingle vextendsingle (4 , 1) = - 1 6.
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