At what points on the curve y=x^2/(2x+5) is the tangent line horizontal?

Question

anonymous · Answer

I first use the derivative (quotient rule) and got:
$$y'=\frac{ 2x(x+5) }{ (2x+5)^2 }$$

callisto · Answer

When a line is a horizontal line, what is its slope?

anonymous · Answer

0?

callisto · Answer

Yup! Finding the derivative of a function is just finding the slope of tangent line to the curve. So, you can set y' = 0 to solve x. That will give you the x coordinate when the tangent line to the curve is a horizontal line.

anonymous · Answer

ohh, thanks!!

aum · Answer

They want points ON the curve.  After solving for x, substitute the x-values into the original equation and find the corresponding y-values and express your answer in the form (x,y).

anonymous · Answer

So x=0,-5?

callisto · Answer

Yes, if the derivative you found is correct lol.

anonymous · Answer

i think soo...? Do you mind checking it?

callisto · Answer

Just checked. It is correct :)

anonymous · Answer

Thank you!! :)

callisto · Answer

Don't forget the corresponding y-coordinates as well :)

anonymous · Answer

Yes, I did. it will be (0,0) and (-5,5)

aum · Answer

(0,0) and (-5, -5)

callisto · Answer

Check again for x=-5. aum has got it right.

anonymous · Answer

oops i did. Thanks you!! @aum @Callisto