Thread: critical numbers

Find the critical numbers of the function.

whats the smaller value and the larger value?

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

Originally Posted by break

Find the critical numbers of the function.

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.

okay so







then




not sure if i got this part right.

Originally Posted by break

Find the critical numbers of the function.

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

those are your critical values

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

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