Generalized Mean Value Theorem Suppose the functions f and
Chapter 4, Problem 43(choose chapter or problem)
Generalized Mean Value Theorem Suppose the functions f and g are continuous on 3a, b4 and differentiable on 1a, b2, where g1a2 _ g1b2. Then there is a point c in 1a, b2 at which f 1b2 - f 1a2 g1b2 - g1a2 = f _1c2 g_1c2 . This result is known as the Generalized (or Cauchys) Mean Value Theorem. a. If g1x2 = x, then show that the Generalized Mean Value Theorem reduces to the Mean Value Theorem. b. Suppose f 1x2 = x2 - 1, g1x2 = 4x + 2, and 3a, b4 = 30, 14. Find a value of c satisfying the Generalized Mean Value Theorem.
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