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Unformatted text preview: vu (tv2894) Homework 14 (Section 4.2) miner (55096) 1 This printout should have 4 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Determine if Rolles Theorem can be ap plied to f ( x ) = x 2 + 2 x 8 x + 6 on the interval [ 4 , 2], and if it can, find all numbers c satisfying the conclusion of that theorem. 1. c = 2 , 10 2. c = 2 , 1 3. c = 2 correct 4. c = 2 3 5. c = 1 6. Rolles Theorem not applicable Explanation: For a function of the form F ( x ) = ( x a )( x b ) x m we see that F ( a ) = F ( b ); in addition, since the denominator is zero only at x = m , F is continuous and differentiable on ( , m ) uniondisplay ( m, ) . Thus Rolles Theorem can be applied to F on the interval [ a, b ] so long as m does not belong to ( a, b ). When f ( x ) = ( x + 4)( x 2) x + 6 , therefore, Rolles Theorem applies to f on the interval [ 4 , 2]. Now, by the Quotient Rule, f ( x ) = (2 x + 2)( x + 6) ( x 2 + 2 x 8) ( x + 6) 2 = x 2 + 12 x + 20 ( x + 6) 2 .....
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 Fall '10
 Gualdini
 Calculus

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