Question

**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, dÂ2y/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. **NOTE: **This polynomial is raised to the **fourth** 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 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, day/dx2 = 0. Be sure to find the sign (+ or -) of

dy/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 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 quot;Bonus Opportunityquot; 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 the

fourth 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.

Y =-2X4 +5X3 -5

X

-.50 -.25 0 .25

.875

1.25 1.50 1.75 1.875 2.00

2.25

Y

dv/dx

12y/dx2

Label Point

(MAX, MIN, INF)

Twenty point Bonus Opportunity (creditable toward the maximum of 600 exercise points). Use

the eleven 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

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