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Section 4.1-solutions - to(aqt73 Section 4.1 isaacson(55826...

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to (aqt73) – Section 4.1 – isaacson – (55826) 1 This print-out should have 5 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Find all the critical points of f when f ( x ) = x x 2 + 25 . 1. x = 0 , 5 2. x = - 25 , 25 3. x = - 5 , 0 4. x = - 5 , 25 5. x = - 25 , 5 6. x = - 5 , 5 correct Explanation: By the Quotient Rule, f ( x ) = ( x 2 + 25) - 2 x 2 ( x 2 + 25) 2 = 25 - x 2 ( x 2 + 25) 2 . Since f is differentiable everywhere, the only critical points occur at the solutions of f ( x ) = 0, i.e. , at the solutions of 25 - x 2 = 0 . Consequently, the only critical points are x = - 5 , 5 . 002 10.0points Find all the critical points of the function f ( x ) = 2 sin x - | x | on the interval ( - π, π ). 1. x = 0 2. x = - π 3 , 0 , 2 π 3 3. x = - 2 π 3 , π 3 4. x = - 2 π 3 , 0 , π 3 correct 5. x = - π 6 , 0 , π 6 6. x = - 5 π 6 , - π 6 , 0 , π 6 , 5 π 6 7. x = - 5 π 6 , 0 , 5 π 6 8. x = - π 3 , 2 π 3 Explanation: Since | x | is differentiable everywhere except at x = 0, while sin x is differentiable for all x , the point x = 0 is a critical point of f and all other critical points will be the solutions of f ( x ) = 0. Now f
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