Question

Calculate the Y values corresponding to the X values given below. Find the critical values for...

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.

                                                Y = X3 –X2 +3

                                                                                                                                                           

X

-.333

-.25

0

.25

.333

.667

1

Y

dy/dx

d2y/dx2

Label Point

(MAX, MIN, INF)

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