Part 1: Given the picture below answer the following questions:
1) The graph above is for the function. If you did not have the picture to look at but wanted to sketch it what points on the graph would be valuable points to know the locations of? The maxima, the minima, and the inflection points
2) What information about the shape of the graph or behavior of the curve in relationship to the x-axis would be important to have to be sure your sketch was as accurate as possible? The concave upward and the concave downward.
Part 2: Now that we know what kinds of information we are looking for we need to discover how to find it. For each question below set the function equal to zero and solve for x. Then, plug those values back into f(x) and locate where the resulting point(s) exists on the graph at the top of page one. For questions 2 and 3 see if you can find a way to use the point(s) you found to break the graph into intervals that will help you fill out the tables. Also, using either or both of your textbook and lecture notes find the first and second derivative tests and determine how they can help you.
1) What information about its graph can we determine from the function itself? Hint: Think back to our discussion of limits. Use the function above to find this information. It has three x intersepts. One maxima and one minima. One concave downward and one concave upward. The x intersepts are (0,0)(-2,0)(10,0)
2) What information about its graph can we determine from the 1st derivative of the function? The first derivative of our function is Points of maxima and minima
X-value in interval
Sign of f’(x) at chosen value
Conclusion about increasing/decreasing behavior
3) What information about its graph can we determine from the 2nd derivative of the function? The second derivative of our function is . The points of inflection are...
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