At what points on this curve is the tangent line horizontal?

[physphys]

Homework Statement

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

Homework Equations

Quotient rule

The Attempt at a Solution

I figured out the derivative which is
2x(2x+5) - 2x^2
-----------------
(2x+5)^2

I also know that for the equation of the tangent to be horizontal, it needs to have a slope of 0, so y' = 0

Therefore I tried to do 2x(2x+5) - 2x^2 = 0, and I got 2x^2 + 10x = 0 which means that x must be -5. However when I put it into the calculator, it doesn't agree with me, so I went wrong somewhere.

Thanks in advance!

 

[HallsofIvy]

I have no idea what you mean by "put it into the calculator". However, "2x^2+ 10x= 0" does NOT mean "that x must be -5". How did you get that?

 

[physphys]

I got a ti84, and i can draw a tangent line and it'll tell me the formula, so when I drew a tangent line through -5, the line was not horizontal completely. If you plug in -5 into 2x^2 + 10x= 0, it works out, but when you plug it back into the first one you don't get 0.

 

[Mark44]

There are two critical numbers; x = -5 is one of them.

If you substitute x = -5 into y = x²/(2x + 5), you'll get the y value at one of the points where the tangent is horizontal.

 

[physphys]

There are two critical numbers; x = -5 is one of them.

If you substitute x = -5 into y = x²/(2x + 5), you'll get the y value at one of the points where the tangent is horizontal.

But the calculator disagrees with the fact that x = -5 is one of them, and also how can I find the other point?

 

[Mark44]

I have no idea what you're entering into the calculator, so I can't say that its objections are valid.

To find the other critical number, find both solutions of 2x² + 10x = 0.

I hope you aren't doing this:

2x² = - 10x

and then dividing both sides by 2x.

 

[hapefish]

Wolfram Alpha gave the following graph when asking for the tangent line to y=(x^2)/(2x+5) at x=-5. If your graph doesn't look like this then you have either told us the wrong function or mis-entered something into your calculator.


http://www.wolframalpha.com/input/?i=tangent+line+to+y+%3D+%28x^2%29%2F%282x%2B5%29+at+x%3D-5