Assume that f ' (x)≤ M for a ≤ x ≤ b. One can show by the Mean ValueTheorem that f (b) − f (a) ≤ M (b − a), and thus f (a) − M(b − a) ≤ f(b) ≤ f (a) + M(b − a). Using this fact, determine a lower bound and an upper bound for 17^1/2 (Hint: Let f (x) = x^1/2, a = 16, and b = 17, and then find bounds for f (17) = 17^1/2.First, find a reasonable value for M: M = Then fill in the blanks: ≤ f (17) ≤

Assume that f ' (x)≤ M for a ≤ x ≤ b. One can show by the Mean ValueTheorem that f (b) − f (a) ≤ M (b − a), and thus f (a) − M(b − a) ≤ f(b) ≤ f (a) + M(b − a). Using this fact, determine a lower bound and an upper bound for 17^1/2 (Hint: Let f (x) = x^1/2, a = 16, and b = 17, and then find bounds for f (17) = 17^1/2.First, find a reasonable value for M: M = Then fill in the blanks: ≤ f (17) ≤

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 78E

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