Calculate the Y values corresponding to the X values givenbelow.  Find the critical values for Xfor the given polynomial by finding the X values among those givenwhere the first derivative, dy/dx = 0 and/or X values where thesecond derivative, d­²y/dx² =0.    Be sure to find the sign (+ or -)of  dy/dx and of d²y/dx² at all Xvalues. Reference Lesson 13 and the text Appendix A (pp 694 – 698),as needed.  Using the first and second derivative testswith the information you have calculated, determine which Xvalue(s) represent maximums (MAX), which minimums (MIN) and whichinflection points (INF).  Label the qualifying X value assuch.  Attach work to convince me you carried out thesecalculations.  An Excel spreadsheet can make calculationseasier.  If used, please attach the spreadsheet file andupload it with the rest of your work so that I can examine yourformulas.  The beginning and ending X values below arenot to be considered critical values.  In the space afterthe “Bonus Opportunity” write the first derivative (dy/dx) and thesecond derivative (d²y/dx²₎ youused or you will not receive credit for them.

                                                Y= 50 + 15X – 6.5X² – 2/3X³

                                                                                                                                                            

X	-8.5	-7.5	-6.5	-3.5	-3.25	-3	0	1	2
Y
dy/dx
d2y/dx2
Label Point (MAX, MIN, INF)

Use the nine X values and their Y values you found above (whichinclude the critical values) to help neatly sketch the graph ofthis polynomial function over the range of X values given. Yoursketch must be consistent with the tabled values above (whichmeans, if you claim a certain X value is a maximum, then the graphof it should show this same value as amaximum.  Similarly, if you claim an X value is aninflection point, then the graph of it should show it to beso.  A minimum should graph as a minimum,too.  The point is, if you figure out how the derivativesSIGNAL which X values are critical points, the graph of the valuesshould show them as such.)