Question

Find an equation for the line tangent to the graph of f(x)=sqrt(x)/5x+5 at the point (3,f(3))

Answer 1

find \(f'(3)\) that is your slope
then your point is \((3,f(3))\) point slope formula will give you the equation for the line

Answer 2

it will be nice and ugly since \(f(3)=\frac{\sqrt{3}}{20}\) if i am reading your function correctly

Answer 3

-1/80sqrt(3)?

Answer 4

is it \(f(x)=\frac{\sqrt{x}}{5x+5}\) ?

Answer 5

yes.. i got that ^ for f'(3)

Answer 6

(1-3)/(10 sqrt(3) (1+3)^2)

Answer 7

yeah i guess that is right
http://www.wolframalpha.com/input/?i=+%281-3%29%2F%2810+sqrt%283%29+%283%2B1%29^2%29

Answer 8

that's the slope?

Answer 9

yup
ugly huh?

Answer 10

sqrt(3)/20=(-1)/(80sqrt(3))(3)+b?

Answer 11

got it! thanks!

Answer 12

you need an \(x\) and a \(y\) in your answer
\[y-f(3)=f'(3)(x-3)\]

Answer 13

yw