In the following the symbol for the first derivative is dy/dx or Y and the symbol for the second derivative is day/dx' or Y", all of which are standard symbols. Y=-1 +X +X2 -x3 X -.667 -.333 0 .333 .667 1 1.333 Y dy/dx day/dx 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. 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 worksheet, show how you calculated its Y value. Use these XY pairs also if you chose to do the bonus option. 2. Find the critical values among the given X values by: a. 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). 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 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 d'y/dx- here Show how you found this second derivative on the worksheet (this is half the credit for this question). b. Using the second derivative from (3a) solve it for all the X values that make day/dx equal zero. Show your work on the worksheet and also write "0" in the cell of the day/dx 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). 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/dx values? There may be none, one, or two maximums. Write your values below:Value of X Value of its dly/dx2 5. Are there minimums among the X, Y pairs? If so, then the pair's dy/dx = 0 and also its day/dx will be a positive (+) 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 minimums. Write your values below: Value of X Value of its d'y/dx 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/dx- 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: Value of X Value of its d'y/dx2 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