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.

1 comment:

MrSiwWy said...

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:

A = f(x)
B = f''(x)
C = unrelated
D = f'(x)