Using the product rule, we find:
Find the critical numbers of the function
x^(4/5) * ((x-4)²)
I used the chain rule. Got 8/5x^(-1/5) * (x-4).
That would give me critical points of 0 and 4.
Where does this 8/7 value come from?
Thanks again guys!!
Also I'm sure many of you are about to watch football so good luck!! (Go Skins!!)
To explain a little further, you use the chain rule for compositions - functions of the form f(g(x)), and the product rule for products - functions of the form f(x)g(x). For most functions you don't get to choose; you have to use whichever is appropriate.
The function you have is a product, so you use the product rule:
You actually use the chain rule for , though you probably do it without really thinking. It is the composition of and . So and by the chain rule, .
and then what MarkFL2 said.