Michael J. answered • 08/31/15
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Mastery of Limits, Derivatives, and Integration Techniques
Sketch the graphs of the 2 functions on the same coordinate system. By doing so, you will see the functions forming a closed region with left and right boundaries when they intersect. These boundaries are the intervals in which you will calculate the definite integral. Then you will find the area under the curve by integrating the function that establishes a curve-like feature.
Michael J.
You will need to utilize the derivative tests when you learned how to sketch non-linear graphs. Use first derivative test to find the minimum and maximum points. Use second derivative test to determine where the graph changes concavity. You will also need to find the x-intercepts and y-intercepts as well. Once you have all the information needed, use it to sketch the graphs. As for where the graphs intersect, you will be able to see after you graphed them.
For first derivative test:
f'(x) = 0
x gives you possible locations of minimum and maximum points.
For second derivative test:
f"(x) = 0
x gives you possible locations of inflection points. Inflection points indicate change in concavity.
Does this info help a little bit?
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08/31/15
Stephanie H.
08/31/15