Question

Find the equation of the tangent line to the curve y=(sqrt(x))/(7x+7) at the point (1, f(1)).

Answer 1

Find the derivative of the function. The result will be a function that tells you the slope of the tangent at a given \(x\).

Answer 2

Do you need help?

Answer 3

i get 1/14 as the slope. that's with using the x=1 as the f'(x)

Answer 4

so does the "point" change from (1,f(1)), to (1,1/14)?

Answer 5

Hmm, no -- the derivative is the function that tells you the slope of the tangent at any point, so you have to find f'(1). What you got was f(1).

Answer 6

oh, in that case than I get 0

Answer 7

That is correct!

Answer 8

so the slope is 0

Answer 9

Exactly!

Answer 10

but how do I write a line equation without a slope

Answer 11

its y=mx+b or y-y1=m(x-x1)

Answer 12

Oh, we had to find the equation of the tangent.

Answer 13

You know the slope, and a point of the line.

Answer 14

That is, (1,0)

Answer 15

yeah

Answer 16

So use y - y1 = m(x - x1)

Answer 17

y-0=0(x-1)?

Answer 18

Yup! Or y = 0.

Answer 19

so what would the equation of the line be?

Answer 20

y = 0.

Answer 21

my math program is telling me y=0 is incorrect...

Answer 22

Hmm... I wonder why.

Answer 23

Whoops!

Answer 24

?

Answer 25

The point is not (1,0) but (1,1/14). Sorry.

Answer 26

so would the equation then look like this? y-1/14=0(x-1)

Answer 27

then y-1/14=0
then y=1/14

Answer 28

Indeed!

Answer 29

thank you