Find all critical numbers for the function f(x) =

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- Jul 26th 2007, 09:16 AMSamanthafind critical numbers
Find all critical numbers for the function f(x) =

- Jul 26th 2007, 09:42 AMred_dog
The critical points are the roots of .

So, you have to calculate and solve the equation . - Jul 26th 2007, 10:05 AMPlato
Definitions do differ. In North America it is common to see the following:

A**critical number**of a function*f*is a number*c*in the domain of*f*at which*f (c)=0*or*f (c)*does not exist. - Jul 30th 2007, 05:05 AMSamantha
I didn't get it =(

- Jul 30th 2007, 05:29 AMgalactus
Plato gave you a good hint. Find f'(x). Where does f'(x) not exist. What makes the denominator equal to 0?.

- Jul 30th 2007, 05:40 AMSamantha
is it

a) 1

b) 1, -3

c) -3

d) 1, -1

e) None of these - Jul 30th 2007, 06:38 AMtopsquark
- Jul 31st 2007, 06:25 AMSamantha
- Jul 31st 2007, 06:54 AMtopsquark
- Jul 31st 2007, 07:13 AMcurvature
- Jul 31st 2007, 07:16 AMtopsquark
- Jul 31st 2007, 07:35 AMcurvature
- Jul 31st 2007, 08:22 AMSamantha
I understand now, thanks =)

- Jul 31st 2007, 08:25 AMPlato
I agree with Curvature that the function has no critical numbers. I do not think that it is a philosophical point.

Here is list of the most widely used calculus texts. I have listed them in order of popularity: Stewart; Larson, Hostetler & Edwards; Hughes-Hallett, Gleason, McCallun; Thomas/Finney; Varberg & Purcell; Smith & Minton; and (out of print) Sallas & Hille. In all of these the definition of**critical number**is exactly as I gave it above. The one exception is found in Thomas/Finney and they require c to be an interior point of the domain. It seems to me this makes a convincing argument that 3 is not a critical number for this function. - Jul 31st 2007, 09:17 AMtopsquark