Worksheet_on_Intermediate_Value_Theorem - CALCULUS BC WORKSHEET ON INTERMEDIATE VALUE THEOREM Work the following on notebook paper On problems 1 \u2013 4(a

Worksheet_on_Intermediate_Value_Theorem - CALCULUS BC...

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CALCULUS BC WORKSHEET ON INTERMEDIATE VALUE THEOREM Work the following on notebook paper. On problems 1 – 4: (a) Determine if the Intermediate Value Theorem holds for the given value of k . (b) If the theorem holds, find a number c for which f c k ( ) = . If the theorem does not hold, give the reason. (c) Draw a sketch of the curve and the line y k = . 1 1 [ ] 0 2 1. ( ) [ ] f x a b k = = = + , , , , 1 5 x 1 3 [ ] 0 2 2. ( ) [ ] f x a b k = = = + , , , , 1 4 x 3. ( ) [ ] 2 f x x x a b k = − − = − = − 3 4 [ ] 2 3 2 , , , , 2 4. ( ) [ ] [ ] f x x a b k = − = − = 9 , , 3, 1 , 2 ______________________________________________________________________________ 5. Given the function ( ) 2 f x x x = + − 2 5. (a) Does f x ( ) = 7somewhere on the interval [ 1, 3 ] ? Use the Intermediate Value Theorem to show why or why not. (b) Does f x ( ) = 12somewhere on the interval [ 1, 3 ] ? Use the Intermediate Value Theorem to show why or why not. 6. Use the Intermediate Value Theorem to show that 3 x x + = 0has a root in the interval [ 1, 2

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