How do you find critical points?

Question

anonymous · Answer

Critical numbers so that I can find absolute min and max.

anonymous · Answer

Find the derivative of the function first.  From there you can set the derivative equal to zero and solve for x

anonymous · Answer

okay so the derivative of my function is 2x+1

anonymous · Answer

2x+1=0

anonymous · Answer

Just solve for x now

anonymous · Answer

-0.5

anonymous · Answer

1/2

anonymous · Answer

-1/2 is right

anonymous · Answer

Keep in mind this is one way to find critical numbers.  
If the derivative has a denominator with an x in it, then just find the value of x that would make the whole denominator equal to zero.  For example if
$$ f'(x) =\frac{ 2x }{ (x-2)^2 }$$
then the critical number would be x=2 since it would cause the denominator to be zero.

anonymous · Answer

Does it only have one critical number?

anonymous · Answer

In the case of your derivative 2x+1, yes, there is only one critical number.  -1/2 is the only number that will make 2x+1=0 true.

anonymous · Answer

What's your original function?

anonymous · Answer

(x^3+1)/(x+1)

anonymous · Answer

Hmm...it doesn't look like the derivative of this function should be 2x+1.  Did you use the quotient rule?