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Chapter 3: Q. 58 (page 290)
Consider the can-making situation in the previous exercise, but suppose that the cans are made with open tops.
If each can must hold 400 cubic inches of liquid, what is the cheapest way to make the cans? What is the most expensive way?
The value of the radius is 3.706 and height is 9.266.
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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.
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.
Prove that the function is increasing on all values of real numbers.
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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.
Sketch the graph of a function f with the following properties:
f is continuous and defined on R;
f has critical points at x = 鈭�3, 0, and 5;
f has inflection points at x = 鈭�3, 鈭�1, and 2.
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