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, d­²y/dx² = 0. Be sure to indicate the sign (+ or -) of dy/dx and of d²y/dx² tabled values. Reference Power Point Lesson 13 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 (-1) and ending X values (.25) below are not to be considered critical values. In the space after the instructions for the “Bonus Opportunity” write the first derivative (dy/dx or Y’). Set this equal to zero and solve for the X values that make it equal to zero. Also write the second derivative (d²y/dx²or Y”)_. Set this equal to zero and solve for the X values that make it equal to zero. Complete the table by following the example on the cover of the Assignment 6 folder and/or in Power Point Lesson 13.   View the scoring rubric to see how point values are awarded for correct calculations.

                                                Y = 3 –X² –X³

X	-1	-.667	-.5	-.333	-.25	0	.25
Y
dy/dx
d2y/dx2
Label Point (MAX, MIN, INF)

Twenty point Bonus Opportunity (creditable toward the maximum of 1000 points). Use the nine X values and their Y values you found above (which include the critical values) to help neatly draw the graph of this polynomial function over the range of X values given.   Alternatively use a spreadsheet to plot it. Your graph 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. If the derivatives signal a X value as a minimum, the graph should show the same 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. Be certain to indicate these critical values with labels on the X axis of your graph.

Answer 1

The top table gives the calculated values and the bttom table shows the formula view of the spreadsheet.

The function has also been plotted as shown below, where the MAX, MIN and INF points are labeled and highlighted.