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HW_4_2

# HW_4_2 - correct to two decimal places f x = x 3 x – 1[0...

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Student Name: Sections 4.2 (Due: Tuesday, 10/23) Description : This homework will help you learn how to apply the Rolle’s Theorem, The Mean Value Theorem and how to obtain information about a function from its derivative. Show all work to get full credit. 1) Find the number c that satisfies the conclusion of Rolle's Theorem. (Give your answer correct to two decimal places.) f ( x ) = cos( 5 x ), c = 2) Find the number c that satisfies the conclusion of Rolle's Theorem. [0, 9 ] c = 3) Find the number c that satisfies the conclusion of the Mean Value Theorem. f ( x ) = 4 x 2 + 2 x + 3, [-1, 1] c = 4) Find the number c that satisfies the conclusion of the Mean Value Theorem. (Give your answer
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Unformatted text preview: correct to two decimal places.) f ( x ) = x 3 + x – 1, [0, 7 ] c = 5) Find the number c that satisfies the conclusion of the Mean Value Theorem. (Give your answer correct to two decimal places.) f ( x ) = e-5 x , [0, 5 ] c = 6) Find the number c that satisfies the conclusion of the Mean Value Theorem. (Give your answer correct to two decimal places.) [1, 4] c = 7) If f ( 2 ) = 5 and f '( x ) ≥ 1 for 2 ≤ x ≤ 7 , how small can f ( 7 ) possibly be? 8) Suppose that 4 ≤ f '( x ) ≤ 5 for all values of x . Complete the inequality below. ≤ f ( 4 ) - f ( 1 ) ≤...
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