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Chapter 3: Q. 15 (page 260)
Explain the difference between two antiderivatives of the function.
The two functions are antiderivatives of each other if their difference is constant.
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Use the first derivative test to determine the local extrema of each function in Exercises 39- 50. Then verify your algebraic answers with graphs from a calculator or graphing utility.
For each set of sign charts in Exercises 53鈥�62, sketch a possible graph of f.
For the graph of f in the given figure, approximate all the values x 鈭� (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.
Determine whether or not each function f in Exercises 53鈥�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 鈭� (a, b) that satisfy the conclusion of the Mean Value Theorem.
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.
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