Math Help - critical numbers

1. critical numbers

Find the critical numbers of the function. $f(x) = x^3 + x^2 - x$

whats the smaller value and the larger value?

the derivative of this is
3x^2+2x-1 but i get lost right after.

2. Originally Posted by break
Find the critical numbers of the function. $f(x) = x3 + x2 - x$

whats the smaller value and the larger value?

the derivative of this is
3x^2+2x-1 but i get lost right after.
critical values occur where f'(x) = 0 or where f'(x) is undefined.

set the above derivative equal to 0 and solve for the critical values of x, then determine extrema.

3. okay so

$3x^2+2x-1=0$
$2x-1=3x^2$
$-1=3x^2/2x$
$-1=3x/2$
$0 = (3x+2)/2$

then

$0 = 3x+2$
$-2/3 = x$

not sure if i got this part right.

4. Originally Posted by break
Find the critical numbers of the function. $f(x) = x^3 + x^2 - x$

whats the smaller value and the larger value?

the derivative of this is
3x^2+2x-1 but i get lost right after.

f(x)=(x^3)+(x^2)-x
f'(x)=(3x^2)+(2x)-1

set that equal to zero. you will have to factor the polynomial to get

(3x-1)(x+1)=0

so

3x-1=0
3x=1
x=1/3

x+1=0
x=-1

5. Originally Posted by skeeter
critical values occur where f'(x) = 0 or where f'(x) is undefined.

set the above derivative equal to 0 and solve for the critical values of x, then determine extrema.
from my understanding, critical values are where f'(x)=0

partition numbers are where f'(x)=0 or is undefined

6. Originally Posted by propjohn
from my understanding, critical values are where f'(x)=0

partition numbers are where f'(x)=0 or is undefined

Pauls Online Notes : Calculus I - Critical Points