SOLUTION: Find the maximum value of the function f(x) = x/2 + 2/x in interval [1, 6]?

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Question 1184290: Find the maximum value of the function f(x) = x/2 + 2/x in interval [1, 6]?
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
===> . Letting ===> x = 2. (x ∈ [1,6]).

and ===> there is local minimum at x = 2.

Therefore absolute max exists at either interval endpoint.

f(1) = 2.5 and f(6) = 10/3.

Hence max value of f(x) is 10/3, which can be found at x = 6.
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Alternatively, knowing that for a,b > 0

===> , with equality happening only for x = 2.
Hence there is minimum of 2 at x = 2. Absolute max then exists at either interval endpoint of [1,6],
and we get the same conclusion as in previous calculus approach.

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