Finding tangent and normal lines to y = √x/(x+1) at (4, 0.4)

[QuarkCharmer]

Homework Statement

Find the tangent and normal line through the curve at the given point.
$$y = \frac{\sqrt{x}}{x+1}$$
Through point (4, 0.4)

Homework Equations

The Attempt at a Solution

Now, I calculate y' to be:

$$y' = \frac{-(x-1)}{2\sqrt{x}(x+1)^2}$$

and so:

y'(4) = (-3/100)

That is the slope at x=4 on the curve y?

 

[TPAINE]

I don't see the problem. The slope is -3/100 at the point (4,f(4))=(4,.4).

 

[QuarkCharmer]

Yeah as soon as I clicked submit I realized what the problem with my thinking was. It's time to take a break for the day..

Thanks for the help!