Find all critical numbers for the function f(x) = $\displaystyle \frac {x-1} {x+3}$

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- Jul 26th 2007, 08:16 AMSamanthafind critical numbers
Find all critical numbers for the function f(x) = $\displaystyle \frac {x-1} {x+3}$

- Jul 26th 2007, 08:42 AMred_dog
The critical points are the roots of $\displaystyle f'(x)$.

So, you have to calculate $\displaystyle f'(x)$ and solve the equation $\displaystyle f'(x)=0$. - Jul 26th 2007, 09:05 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, 04:05 AMSamantha
I didn't get it =(

- Jul 30th 2007, 04:29 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, 04:40 AMSamantha
is it

a) 1

b) 1, -3

c) -3

d) 1, -1

e) None of these - Jul 30th 2007, 05:38 AMtopsquark
- Jul 31st 2007, 05:25 AMSamantha
- Jul 31st 2007, 05:54 AMtopsquark
- Jul 31st 2007, 06:13 AMcurvature
- Jul 31st 2007, 06:16 AMtopsquark
- Jul 31st 2007, 06:35 AMcurvature
- Jul 31st 2007, 07:22 AMSamantha
I understand now, thanks =)

- Jul 31st 2007, 07:25 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, 08:17 AMtopsquark