Question

Asked Oct 9, 2019

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Assume that f^{ }'^{ }(x)≤ M for a ≤ x ≤ b. One can show by the Mean Value

Theorem 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) ≤

Step 1

From the given information, f(x) = x1/2, a = 16 and b = 17, t...

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