6 - MVT Wkst.pdf - Chapter 3 \u2013 Mean Value Theorem WKST Name Understanding IVT MVT and Rolle\u2019s Theorem A Graphing Calculator is allowed for these

# 6 - MVT Wkst.pdf - Chapter 3 u2013 Mean Value Theorem WKST...

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Chapter 3 Mean Value Theorem WKST Name: Understanding IVT, MVT, and Rolle’s Theorem A Graphing Calculator is allowed for these problems. For problems #1 and #2, find the value of c guaranteed by the Mean Value Theorem on the indicated interval such that . 1. on [ 1 , 3 ] 2. on [ -1 , 1 ] 3. Which of the following satisfy the hypotheses of Mean Value Theorem on the interval [ 0 , 2 ] ? I. II. III. 4. Which of the following satisfy the hypotheses of Mean Value Theorem on the interval [ 0 , 3 ] ? Note: this is the same as #3, except the interval is different. I. II. III. a b a f b f c f - - = ) ( ) ( ) ( ' 2 ) ( x x f = 1 ) ( 3 + = x x f x x x f 2 cos sin ) ( + p = 3 2 ) ( - = x x f x x x f 2 ) ( 2 - = x x x f 2 cos sin ) ( + p = 3 2 ) ( - = x x f x x x f 2 ) ( 2 - =
5. Which of the following satisfy the hypotheses of Rolle’s Theorem on the interval [ 0 , 2 ] ? I. II. III. IV. 6. Let fbe continuous for where ( 0 , 13 ) and ( 5 , 3 ) are the endpoints of f. The Intermediate Value Theorem guarantees which of the following?