YAMT: Calculus Question

[speg]

Find y' at the point indicated, where sqrt[x] - sqrt[y] =4. (1,9)

I get y' = sqrt[y] / sqrt [x]. Which at (1,9) would equal 3. But the answer key says -3. Where did that negative come from?

 

[Soccer55]

sqrt[9] = 3 or -3 since 3^2 = (-3)^2
Now, since they say that sqrt[x] - sqrt[y] = 4, you need that 1 - sqrt[y] = 4. This implies -sqrt[y] = 3 which implies that sqrt[y] = -3.

-Tom

 

[zzzz]

sqrt(x^2) = +x or -x

get the correct sign from the second equation.

 

[Syringer]

Hmm, how did you get y' = sqrt[y] / sqrt [x] ?

I'm probably way off because what I get isn't the answer..but don't you have to solve for y in the first equation and take the derivative?

 

[speg]

Doh! So simple, and makes so much sense. Thanks guys. 😎

Edit: Springer you could isolate y, and end up with y' =( sqrt[x]-4 ) / sqrt[x] which would work.

But the other way is using implicit differentiation, which is what we had to use for this lessson.

 

[Soccer55]

Originally posted by: Syringer
Hmm, how did you get y' = sqrt[y] / sqrt [x] ?

I'm probably way off because what I get isn't the answer..but don't you have to solve for y in the first equation and take the derivative?

speg may have been given that y' = sqrt[y]/sqrt[x] in the problem. I didn't bother to check to see if the derivative was right, I just answered his question about the sign 😛

-Tom