Question

Find the equation of the line tangent to the graph of the given function at the point with the indicated x-coordinate.

f(x)=[((sqr x) + 1)/(sqt x) + 3)]; x=4

Answer 1

\[f(x)=\frac{ \sqrt{x}+1 }{ \sqrt{x}+3 }; x=4\]

Answer 2

Differentiate the function ^_^

Answer 3

to find the tangent line?

Answer 4

Look... to find the equation of any line, most of the time, you need a slope and a point.

To find the slope of the tangent line, we need the derivative.^_^

Answer 5

Pro-tip... might be a little too late, but meh...
If you think doing this integral is a little tedious, use this fact to your advantage:
\[\Large \frac{\sqrt x + 1}{\sqrt x + 3}= \frac{\sqrt x + 3 - 2}{\sqrt x + 3}=1 - \frac2{\sqrt x + 3}\]

Answer 6

I get \[f \prime(x)= 1+\frac{ 3x ^{-\frac{ 1 }{ 2 }} }{ 2(x+6\sqrt{x}+9 }-\frac{ x ^{-\frac{ 1 }{ 2 }}(\sqrt{x}+1) }{ 2(x+6\sqrt{x}+9) }\]

Answer 7

Sorry... I'm not good when it comes to troubleshooting someone else's derivative... (these can get pretty messy at times)

Please hold...

Answer 8

Something's off. Try doing it again... you didn't post your solution, so I can't really see where the mistake was. Oh, and don't expand, keep squares as is, they can really reduce headaches ^_^

Answer 9

Oh I though I could just leave it like that

Answer 10

You could... but you might want to reduce your own (and your instructor's) headache by keeping your notation compact.

Anyway, try differentiating instead that one I posted. It's simpler.