AP Calculus (in relation to a family of functions)

I'm enrolled in AP Calculus this year! Woohoo for me!
Anyway, I'm doing some extra work outside of class, and one of the sample test questions I ran into is a bit tricky; I'm having trouble on the last part (Part "d"). Here's the question:
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Part (a) was easy, of course. Graphing, pfft!
Parts (b) and (c) were easy, too; the maximums lie at any point ( -sqrt(b), (2b)sqrt(b) ) and the minimums are at any point ( sqrt(b), (-2b)sqrt(b) )

Part (d), though... hm. I have no idea.
I know that the slope of any line containing the maximum and minimum points of a member of the family is (-2b)... and that's it.

Help me, please!

P.S. ("sqrt" means "square root of")
P.P.S. (If that's unreadable, the function is of the form y=-ax^3 )

a = 2

you have to take the form given: y = -ax^3 and value the maximum and minimum points you have already found... I will show you the minimum one:


form: y = -ax^3 point: (sqrt(b), -2b*sqrt(b))

....substituting the values of x and y in the form:

-2b*sqrt(b) = -a (sqrt(b))^3

-2b*sqrt(b) = -a b*sqrt(b)

cancelling b*sqrt(b):

-2 = -a
a= 2
...

you have to do the same with the maximum....because the question said "and"...

(sorry, I'm always, always late)... If you have any other questions, I'll try to be around
more often...so just PM me or anything...

(Mary Poppins laugh) Ahahahaha!

That makes perfect sense now.

Thanks!

I'm glad it helped... you know? this is the first calculus question I have seen posted here... mmmmm, I want more..... (haha)


well, If you need help with any other problem, be sure to post it....