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Unformatted text preview: to (aqt73) – Section 4.1 – isaacson – (55826) 1 This printout should have 5 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points 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 , 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 10.0 points 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 , , 2 π 3 3. x = 2 π 3 , π 3 4. x = 2 π 3 , , π 3 correct 5. x = π 6 , , π 6 6. x = 5 π 6 , π 6 , , π 6 , 5 π 6 7. x = 5 π 6 , , 5 π 6 8. x = π 3 , 2 π 3 Explanation:...
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This note was uploaded on 06/14/2011 for the course MATH 305G taught by Professor Cathy during the Spring '11 term at University of Texas.
 Spring '11
 Cathy
 Critical Point

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