Lesson17_-_The_Mean_Value_Theorem_ws

Lesson17_-_The_Mean_Value_Theorem_ws - 1 3. Find all...

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Worksheet for Section 4.2 The Mean Value Theorem V63.0121, Calculus I Spring 2010 1. For each of the functions f and intervals [ a,b ] below, try to find a c for which f 0 ( c ) = f ( b ) - f ( a ) b - a . If c cannot be found, explain why the Mean Value Theorem is not contradicted. (i) f ( x ) = x 2 on [ - 1 , 2] (ii) f ( x ) = | x | on [ - 1 , 2] (iii) f ( x ) = 1 x on [ - 1 , 2] 2. Use calculus to show that the equation x 4 + 6 x 2 = 1 has exactly two real solutions.
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Unformatted text preview: 1 3. Find all dierentiable functions F whose derivative is cos x . How do you know youve found them all? s 4. Show that for any positive integer n that 1 n + 1 < ln( n + 1)-ln( n ) < 1 n Hint. Obviously, you want to use the Mean Value Theorem. See if you can recognize f ( b )-f ( a ) b-a someplace. 2...
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Lesson17_-_The_Mean_Value_Theorem_ws - 1 3. Find all...

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