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Chapter 3: Q 40. (page 299)
suppose the sides of a cube are expanding at a rate of inches per minute.
How fast is the volume of the cube changing at the moment that the cube has a side length of inches?
The rate of change in volume is.
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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.
For each set of sign charts in Exercises 53鈥�62, sketch a possible graph of f.
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.
Restate Theorem 3.3 so that its conclusion has to do with
tangent lines.
Use the second-derivative test to determine the local extrema of each function in Exercises . If the second-derivative test fails, you may use the first-derivative test. Then verify your algebraic answers with graphs from a calculator or graphing utility. (Note: These are the same functions that you examined with the first-derivative test in Exercises of Section .)
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