A window through the walls of our classroom. This is an interactive learning ecology for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.
Monday, October 15, 2007
Derivative Assignment
Well here is my derivative assignment finally being posted up on the blog. For the answers to my derivative question, I will create a comment on this very post detailing the answers for my derivative question.
Where A is increasing, function D is the only function that is positive within the same interval(s), therefore D must be the derivative of function A.
Where C is decreasing, there is no function that is negative during the same interval(s), therefore C cannot be the parent function.
Where D is decreasing, and has exetrema (a minimum in this case), function B is negative on these same intervals and has a root respectively. B is the only function with this relationship with D, therefore B is the derivative of D.
Where A changes concavity, B has roots, meaning that B is a candidate as the second derivative of A.
Now, since D is f'(x) of A, and B is f'(x) of D and f''(x) of A, C must be the function with no relationship (which is also very visible under closer inspection). The analyses described above validate the following results:
For the answers to my derivative question, I will create a comment on this very post detailing the answers for my derivative question.
Where A is increasing, function D is the only function that is positive within the same interval(s), therefore D must be the derivative of function A.
ReplyDeleteWhere C is decreasing, there is no function that is negative during the same interval(s), therefore C cannot be the parent function.
Where D is decreasing, and has exetrema (a minimum in this case), function B is negative on these same intervals and has a root respectively. B is the only function with this relationship with D, therefore B is the derivative of D.
Where A changes concavity, B has roots, meaning that B is a candidate as the second derivative of A.
Now, since D is f'(x) of A, and B is f'(x) of D and f''(x) of A, C must be the function with no relationship (which is also very visible under closer inspection). The analyses described above validate the following results:
A = f(x)
B = f''(x)
C = unrelated
D = f'(x)