Find all points where f(x) has a horiztonal tangent line

[SPhy]

1. Given.

F(x) = 4x/(x^2+1)

2. Problem

Find all points (x,y) where the function has a horiztonal tangent line

3. Attempt

I took the derivative of F(x) and came to

(-4x^2+4)/(x^2+1)^2

I set it equal to zero and found an x value of 1. I used that x value and plugged it into the original function, so f(1), and got a Y value of 2, but according to my professor this was not correct. However I asked him this after the test. It was a test question and on the test I stated at no point does the function have a horizontal tangent line.

I figured I was wrong because after the test I redid the problem and came to (1,2). Although as stated, my professor said (1,2) was incorrect. I haven't got my test back, so maybe there was no solution and I did the problem correctly originally, but I think there is a solution.

Thanks!

 

[Dick]

1. Given.

F(x) = 4x/(x^2+1)

2. Problem

Find all points (x,y) where the function has a horiztonal tangent line

3. Attempt

I took the derivative of F(x) and came to

(-4x^2+4)/(x^2+1)^2

I set it equal to zero and found an x value of 1. I used that x value and plugged it into the original function, so f(1), and got a Y value of 2, but according to my professor this was not correct. However I asked him this after the test. It was a test question and on the test I stated at no point does the function have a horizontal tangent line.

I figured I was wrong because after the test I redid the problem and came to (1,2). Although as stated, my professor said (1,2) was incorrect. I haven't got my test back, so maybe there was no solution and I did the problem correctly originally, but I think there is a solution.

Thanks!

There are two points where the function has a horizontal tangent. You've got one. Can you find the other one?

 

[SPhy]

There are two points where the function has a horizontal tangent. You've got one. Can you find the other one?

Hmm I think I forgot to consider the +/- on the square root. So the other point would be (1,-2)?

 

[Dick]

Hmm I think I forgot to consider the +/- on the square root. So the other point would be (1,-2)?

Yes, that's what you forgot. And I'm assuming you meant (-1,-2) and that's just a typo.