Question

How do i find the critical points of
y=(4x+2)/(x^2+3)
Do i use the quotient rule?

Answer 1

if i use the quotient rule and set the derivative to zero i get my critical points right? but do i get the derivative with the quotient rule?

Answer 2

To find the critical points, you have to derive the function once. In your case, you have u/v so you'll have to use the following equation:\[y' = (u'v - uv')/v^2\]

where:

- u = 4x +2
- u' = 4
- v = x^2 +3
- v' = 2x

substitute these in the equation to find the derivative.

After doing that, you'll have to check the 2 conditions needed for the critical points:

1) y' = 0
2) y' = DNE (doesn't exist) , this condition occurs when your denominator is equal to 0.

Give it a try now ^_^

Answer 3

lol, yes roam :)

Answer 4

but don't forget your other condition, when your y' doesn't exist. :)

Answer 5

you're not getting your critical points, you're getting your critical numbers, but in order to get the points, you have to plug the x's you got in the original function to get their y's . When you do so, then you'll get your critical points. ^_^

Answer 6

Oh ok i think I got it, thanks a lot sstarica! :)