[maths] Re: more of calculus
- From: "Ned Granic" <ngranic@xxxxxxx>
- To: <maths@xxxxxxxxxxxxx>
- Date: Tue, 28 Nov 2006 03:52:19 -0700
Thank you Nelson as usual.
Here is the textbook definition of the critical number:
A "critical number" of a function f is a number c in the domain of f such that
f prime(c) = 0 or f prime(c) does not exist.
Then an example is given:
Find the critical numbers of
f(x) = x^3/5 * (4-x)
the product rule gives:
f^'(x) = 3/5x^-2/5 * (4-x) + x^3/5 * (-1)
= [3(4-x)] / [5x^2/5] - x^3/5
= [(4-x)-5x] / [5x^2/5]
= (12-8x) / (5x^3/5).
Therefore,
f^'(x) = 0 when 12-8x = 0, that is, x = 3/2,
and f^'(x) does not exist when x = 0.
So the critical numbers are 3/2 and 0.
Many thanks Nelson for your patience!
Ned
Other related posts:
