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). 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 where dy/dx = 0. There may be none, one, or two such. (this is the other half credit).
In the following the symbol for the first derivative is dy/dx or Y’ and the symbol for the second derivative is d2y/dx2 or Y”, all of which are standard symbols.
Y = 3 –X2 –X3
|
X |
-1 |
-.667 |
-.5 |
-.333 |
-.25 |
0 |
.25 |
|
Y |
3 |
2.8518 |
-2.875 |
2.926 |
2.9531 |
0 |
2.9218 |
|
dy/dx |
-1 |
-0.4437 |
0.25 |
0.333 |
0.3125 |
0 |
-0.6875 |
|
d2y/dx2 |
4 |
2.002 |
1 |
-0.002 |
-0.5 |
-2 |
-3.5 |
A
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).
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 where dy/dx = 0. There may be none, one, or two such. (this is the other half credit).
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