Calculate the Y values corresponding to the X values given below Find the critic

Question

Calculate the Y values corresponding to the X values given below Find the critical values for X for the given polynomial by finding the X values among those given where the first derivative, dy/dx- 0 and/or X values where the second derivative, dyldx2-. Be sure to find the sign (or-) of dy/dx and of d'y/dx2 at all X values. Reference Lesson 13 and the text Appendix A (pp 694 698), as needed. Using the first and second derivative tests with the information you have calculated, determine which X value(s) represent maximums (MAX), which minimums (MIN) and which inflection points (INF). Label the qualifying X value as such. Attach work to convince me you carried out these calculations. An Excel spreadsheet can make calculations easier. If used, please attach the spreadsheet file and upload it with the rest of your work so that I can examine your and ending X values below are not to be considered critical values. In the space after the "Bonus Opportunity" write the first derivative (dy/dx) and the second derivative (d'y/dx2 you used or you will not receive credit for them. formulas. The beginning -667-333 0 333 6671 1,33 dy dx Label Point MAX, MIN, INF Twenty point Bonus Opportunity (creditable toward the maximum of 600 exercise points). Use the seven X values and their Y values you found above (which include the critical values) to help neatly sketch the graph of this polynomial function over the range of X values given. Alternatively use a spreadsheet to plot it. Your sketch must be consistent with the tabled values above (which means, if you claim a certain X value is a maximum, then the graph of it should show this same value as a maximum Similarly, if you claim an X value is an inflection point, then the graph of it should show it to be so. A minimum should graph as a minimum, too. The point is, if you figure out how the derivatives SIGNAL which X values are critical points, the graph of the values should show them as such.)

Explanation / Answer

X -.667 -.333 0 .333 .667 1 1.333 Y -0.925 -1.185 -1 -0.593 -0.184 0 -0.258 dy/dx = 2X-3X2 -2.668 -0.399 0 0.333 -0.00067 1 -2.664 d2y/dx2 = 2-6X 6.002 3.998 2 0.002 -2.002 -4 -5.998

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