Problem Set 11s

2 mean value theorem 43 how derivatives affect graph

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Unformatted text preview: l maximum or a local minimum? 1 Hung Nguyen Problem Set 11 Solution 4.2 Mean Value Theorem 4.3 How Derivatives Affect Graph GE 207C 6. How many real roots does the equation 4. If f (1) = 10 and f '( x ) ≥ 2 for 1 ≤ x ≤ 4 , how small can f ( 4) possibly be? Assume f ( x ) is differentiable everywhere. Solution: From the Mean Value Theorem f (4) − f (1) f ' ( x) ≥ ⇒ f (4) = f (1) + 3 f ' (c ) 3 And since f ' (c) ≥ 2 , then f (4) ≥ 10 + 3(2) = 16 5. If f is a contin...
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This document was uploaded on 02/27/2014 for the course M 408c at University of Texas.

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