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Chapter 3: Q. 53 (page 275)
For each set of sign charts in Exercises 53–62, sketch a possible graph of
The graph is
The given sign chart is
From the given chart,
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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.
role="math" localid="1648370582124"
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 53–62, sketch a possible
graph of f.
Sketch careful, labeled graphs of each function f in Exercises 63–82 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.
Sketch the graph of a function f with the following properties:
f is continuous and defined on R;
f(0) = 5;
f(−2) = −3 and f '(−2) = 0;
f '(1) does not exist;
f' is positive only on (−2, 1).
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