I'm having a tough time with finding f'' so that I can determine the inflection points on the graph of a function. I've found f' which is:

(4-x)/(x^(1/3) (6-x)^(2/3) )

But my f'' is different from f'' provided in the text book. Can someone help me finding f''?

Question

I'm having a tough time with finding f'' so that I can determine the inflection points on the graph of a function.  I've found f' which is:

(4-x)/(x^(1/3) (6-x)^(2/3) )

But my f'' is different from f'' provided in the text book.  Can someone help me finding f''?

anonymous · Answer

Is this one same as your book? http://www.wolframalpha.com/input/?i=%284-x%29%2F%28x^%281%2F3%29%286-x%29^%282%2F3%29%29

anonymous · Answer

Yup, it is

anonymous · Answer

The thing is, looking at the that solution, it uses product rule first.  Perhaps that's what I should be doing instead of using quotient rule first but the solution SHOULD be the same, should it not?

anonymous · Answer

... considering the definition of the derivative lim h->0, etc ...

anonymous · Answer

Sure, sometimes it is the same but not obviously so...

anonymous · Answer

This is the problem that I often have with calculus.  What rule to apply, when to apply them and in what order

anonymous · Answer

As a general rule, try and do the easiest operation first.

Usually, not always, product is easier than quotient.