Chapter 3: Q. 86 (page 276)
In Exercises 83–86, use the given derivative to find any local extrema and inflection points of f and sketch a possible graph without first finding an formula for f .
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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.
For the graph of f in the given figure, approximate all the values x ∈ (0, 4) for which the derivative of f is zero or does not exist. Indicate whether f has a local maximum, minimum, or neither at each of these critical points.
Explain the difference between two antiderivatives of the function.
The cost of manufacturing a container for frozen orange juice is cents, where is the height of the container in inches. Your boss claims that the containers will be the cheapest to make if they are inches tall. Use Theorem 3.3 to quickly show that he is wrong.
Determine whether or not each function f in Exercises 53–60 satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b]. For those that do, use derivatives and algebra to find the exact values of all c ∈ (a, b) that satisfy the conclusion of the Mean Value Theorem.
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