Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of.

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Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. {image} c = - 30 c = - 38 c = - 22 c = 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Find the exact values of the numbers c that satisfy the conclusion of The Mean Value Theorem for the function f ( x ) = x 3 - 2x for the interval [ - 2, 2 ]. {image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Verify that the function satisfies the hypotheses of The Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusion of The Mean Value Theorem. {image} {image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

If f ( 3 ) = 11 and {image} for {image} , how small can f ( 9 ) be? 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

x = 270 mi / h2 x = 278 mi / h2 x = 263 mi / h2 x = 256 mi / h2 1. 2. At 5:00 P.M. a car's speedometer reads 15 mi/h. At 5:15 it reads 79 mi/h. At some time between 5:00 and 5:15 the acceleration is exactly x mi / {image} . Find x. x = 270 mi / h2 x = 278 mi / h2 x = 263 mi / h2 x = 256 mi / h2 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50