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4.2 Mean Value Thm

4.2 Mean Value Thm. Rolle’s Theorem: f is continuous on [ a , b ] f is differentiable on ( a , b ) f ( a ) = f ( b ) Then  a # c in ( a , b ) such that f  ( c ) = 0. Ex 1: Find all c ’s that satisfy Rolle’s Thm: 6  x  0. Mean Value Theorem.

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4.2 Mean Value Thm

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  1. 4.2 Mean Value Thm • Rolle’s Theorem: • f is continuous on [a, b] • f is differentiable on (a, b) • f (a) = f (b) • Then  a # c in (a, b) such that f  (c) = 0.

  2. Ex 1: Find all c’s that satisfy Rolle’s Thm: 6  x  0

  3. Mean Value Theorem • f is continuous on [a, b] • f is differentiable on (a, b) • Then  a # c in (a, b) such that

  4. Ex 2: Verify that f(x) satisfies the MVT in the interval. Then find all c’s that satisfy the MVT: 0  x  2

  5. HW – 4.2 pg. 2931, 3, 5, 10, 11, 13, 15, 23, 25, 35

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