125% + EB A View Zoom Add Page Insert Table Chart Text Shape Media Comment Share Format Document Text DERIVATIVE APPLICATION EXERCISE List Paragraph* Name Due (11) (Worth 50 points + 20 point optional bonus) In the following the symbol for the first derivative is dy/dx or Y' and the symbol for the second Style Layout More derivative is day/dx2 or Y", all of which are standard symbols Y = X3 -X2 +3 Font X -.333 -.25 0 .25 .333 .667 Times New Roman C Regular C 12 pt dy/dx B U S day/dx2 Character Styles None* A function is given above. The table gives several pre-selected values of the independent variable (X). Use all of these to have enough to answer questions for this assignment. Text Color 1. Calculate the Y value corresponding to each X value in the table. Write the Y value and its sign (+ or -) calculated in the cell below its X value. Pick any three of the X values and on a separate E E E worksheet, show how you calculated its Y value. Use these X, Y pairs also if you chose to do the bonus option. E 2. Find the critical values among the given X values by: > Spacing 1.1 . Correctly finding the first derivative of the given function. Write dy/dx here Show how you found the derivative on the worksheet (this is half the credit for this question). > Bullets & Lists Imported Style 1* v b. Using the derivative from (2a) solve it for all the X values that make the derivative equal zero. Show your work on the worksheet and also write "0" in the cell of the dy/dx row for the X value Drop Cap where dy/dx = 0. There may be none, one, or two such. (this is the other half credit). 3. Find additional critical values among the X values by: a. Correctly finding the second derivative of the given function. Write day/dx2 here Show how you found this second derivative on the worksheet (this is half the credit for this question . Using the second derivative from (3a) solve it for all the X values that make day/dx2 equal zero. Show your work on the worksheet and also write "0" in the cell of the day/dx2 row for the X value(s) where day/dx2 = 0. There may be one, or two such. (this is the other half credit). Read the signals given by the critical derivative values above. (NOTE: do not consider the first or the last X value as being among the critical values).125% EB A Format View Zoom Add Page Insert Table Chart Text Shape Media Comment Share Document Text List Paragraph* 4. Are there maximums among the X, Y pairs? If so, then the pair's dy/dx = 0 and also its day/dx2 will be a negative (-) value for each such X, Y pair. What are the X values and also the day/dx2 values? There may be none, one, or two maximums. Write your values below: Style Layout More Value of X Value of its day/dx2 Font Times New Roman C Regular C 12 pt B U S 5. Are there minimums among the X, Y pairs? If so, then the pair's dy/dx = 0 and also its day/dx2 will be a positive (+) value for each such X, Y pair. What are the X values and also the day/dx2 values? Character Styles None* There may be none, one, or two minimums. Write your values below: Value of X Value of its day/dx2 Text Color E E E E 6. Are there inflection points among the X, Y pairs? If so, then the pair's dy/dx may or may not equal zero. However, day/dx2 at each will be zero (0) for each such X, Y pair. What are the X values and also the day/dx2 values? There may be one, or two inflections. Write your values below: > Spacing 1.1 Value of X Value of its day/dx2 > Bullets & Lists Imported Style 1* v Drop Cap Av References: A tutorial at the top of the Blackboard page that contains the twelve versions and also Power Point lesson 13. Twenty point optional bonus opportunity. If done, submit along with the above using the same Gold submission link. Using all X, Y pairs tabled above, plot them. Scale the axis's so that the maximum(s), minimum(s) and inflection(s) are clearly obvious. Indicate numerical values on each axis. Label each maximum, minimum, and inflection point as such on the plot along with its X and Y values. EXAMPLE: Suppose at X = 3.00 and Y = 11.00, you decide this point is an inflection. Then write (3, 11)INF at this point on the graph. You may plot this graph with Excel (but still label the various critical points). Your plot must show each maximum, minimum, and inflection point found in the six previous steps (if labeling is omitted,125% + EB A Share Format Document View Zoom Add Page Insert Table Chart Text Shape Media Comment zero. However, day/dx2 at each will be zero (0) for each such X,Y pair. What are the X values and Text also the day/dx2 values? There may be one, or two inflections. Write your values below: Value of X Value of its day/dx2 List Paragraph* Style Layout More References: A tutorial at the top of the Blackboard page that contains the twelve versions and also Font Power Point lesson 13. Times New Roman C Regular C Twenty point optional bonus opportunity. If done, submit along with the above using the same Gold 12 pt submission link. Using all X, Y pairs tabled above, plot them. Scale the axis's so that the B U S maximum(s), minimum(s) and inflection(s) are clearly obvious. Indicate numerical values on each Character Styles None* axis. Label each maximum, minimum, and inflection point as such on the plot along with its X and Y values. EXAMPLE: Suppose at X = 3.00 and Y = 11.00, you decide this point is an inflection. Then write (3, 11)INF at this point on the graph. Text Color You may plot this graph with Excel (but still label the various critical points). Your plot must show each maximum, minimum, and inflection point found in the six previous steps (if labeling is omitted, E E E E > Spacing 1.1 > Bullets & Lists Imported Style 1* v Drop Cap we will not guess which is what - you must tell us). The scoring rubric and scoring for this bonus opportunity will be shown as a separate exercise in My Grades. derivative_app11.docx 10012020