DERIVATIVE APPLICATION

EXERCISE

Name ______________________ Due __________ (worth 50 points + 20 bonus points)

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, d2y/dx2 = 0. Be sure to find the sign (+ or -) of dy/dx and of d2y/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 formulas. The beginning 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 (d2y/dx2) you used or you will not receive credit for them. This polynomial is raised to the power. You should find among the X values below two inflection points and only one X value which is a Maximum or a Minimum, but not both.

DERIVATIVE APPLICATION EXERCISENameDue(worth 50 points + 20 bonus points)Calculate the Y values corresponding to the X values given below. Find the critical values for X forthe 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, day/dx2 = 0. Be sure to find the sign (+ or -) ofdy/dx and of d’y/dx 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 whichinflection points (INF). Label the qualifying X value as such. Attach work to convince me youcarried out these calculations. An Excel spreadsheet can make calculations easier. If used, pleaseattach the spreadsheet file and upload it with the rest of your work so that I can examine yourformulas. The beginning and ending X values below are not to be considered critical values. In thespace 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. NOTE: This polynomial is raised to thefourth power. You should find among the X values below two inflection points and only one Xvalue which is a Maximum or a Minimum, but not both.Y =-2X4 +5X3 -5X-.50 -.25 0 .25.8751.25 1.50 1.75 1.875 2.002.25Ydv/dx12y/dx2Label Point(MAX, MIN, INF)Twenty point Bonus Opportunity (creditable toward the maximum of 600 exercise points). Usethe eleven X values and their Y values you found above (which include the critical values) to helpneatly sketch the graph of this polynomial function over the range of X values given. Alternativelyuse a spreadsheet to plot it. Your sketch must be consistent with the tabled values above (whichmeans, if you claim a certain X value is a maximum, then the graph of it should show this samevalue as a maximum. Similarly, if you claim an X value is an inflection point, then the graph of itshould show it to be so. A minimum should graph as a minimum, too. The point is, if you figure

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