Homework 14

# Homework 14 - vu(tv2894 – Homework 14(Section 4.2 –...

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Unformatted text preview: vu (tv2894) – Homework 14 (Section 4.2) – miner – (55096) 1 This print-out should have 4 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Determine if Rolle’s 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. Rolle’s 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 Rolle’s 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, Rolle’s 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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Homework 14 - vu(tv2894 – Homework 14(Section 4.2 –...

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