Question

Consider the curve given by
y = x/(y+d)

(a) Find the slope of the tangent line to the curve at the point (0, 0). Your answer will have d in it.



(b) Find the equation of the tangent line to the curve at the point (0, 0). Your answer will have d in it.

Answer 1

did you study derivatives yet ?

Answer 2

yes i have.
we're doing implicit differentiation.

Answer 3

slope = dy/dx

equation of tangent line at point(x1,y1)
\[y = \frac{dy}{dx}(x-x_1) + y_1\]

Answer 4

so i just plug in 0 for x1 and y1 since it has to be tangent at pt(0,0)?

Answer 5

i would multiply the "y+d" over before differentiating

--> y^2 + dy = x

Answer 6

yes ^^

Answer 7

honestly i find y=mx+b much easier

Answer 8

same here because once i find the derivative i get 2y dy/dx +1=1 so that would give me 2y dy/dx and i don't know what to do with that

Answer 9

what do i do once i find the derivative? i still don't have an equation with d in it :/

Answer 10

not quite, the differentiation gives

--> 2y y' + dy' = 1

Answer 11

and then solve for y' and substitute the (x,y) into the derivative to get the value for slope

Answer 12

since there's no x in the derivative would i just ignore the x value?

Answer 13

yes, but you would still plug in the "y" value

Answer 14

okay so i got y'(2y+d)=1 --> 1/2y+d=y' at pt (0,0) -->1/(2(0)+d) = 1/d = y'…?

Answer 15

correct

slope = 1/d

Answer 16

so to find the tangent line i now just use the formula --> y-y1=y'(x-x1) --> y=y'(x-x1)+y1 using the values (0,0) for x and y?

Answer 17

i got 1/dx

Answer 18

thank you so much for your help! it was actually easier than i thought it was going to be! I always make things harder than they are. have a good night!!

Answer 19

yw :)