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Chapter 3: Q. 26 (page 288)
Use optimization techniques to answer the questions in Exercises 25鈥�30.
Find two real numbers x and y whose sum is and whose product is as small as possible.
The two real numbers are and .
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Use a sign chart for to determine the intervals on which each function is increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.
Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of and examine any relevant limits so that you can describe all key points and behaviors of f.
For each graph of f in Exercises 49鈥�52, explain why f satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b] and approximate any values c 鈭� (a, b) that satisfy the conclusion of the Mean Value Theorem.
Restate the Mean Value Theorem so that its conclusion has to do with tangent lines.
In Exercises 83鈥�86, use the given derivative to find any local extrema and inflection points of f and sketch a possible graph without first finding a formula for f.
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