Question

If x3 + y3 = 9 and dx/dt = -3, then what is dy/dt when x = 1 and y = 2?

Answer 1

@RyanRyan What is the dx/dt there for?

Answer 2

Regardless, @satellite73 has pretty much showed you exactly what to do.

Answer 3

actually i was completely wrong!!

Answer 4

no idea, it threw me off

Answer 5

1. Differentiate both sides with respect to x
2. Plug in x = 1 and y = 2.
3. Solve for y'.

Done.

Answer 6

Wait what? is there more to this problem? lol

Answer 7

Oh wait I get it. x and y are functions of t. Lol I forgot about that.

Answer 8

no no i made a mistake by not reading properly
you are supposed to assume that BOTH \(x\) and \(y\) are some unknown functions of \(t\)

Answer 9

\[3x^2x'+3y^2y'=0\] is the start

Answer 10

thats the exact problem.. It is extra credit so maybe she is making it confusing? or its just late, I dont know, this particular problem is multi choice too

Answer 11

then pout \(x'=-3,x=1,y=2\) and solve for \(y'\)

Answer 12

no problem is perfectly normal
you are not asked for \(\frac{dy}{dx}\) but rather \(\frac{dy}{dt}\)

Answer 13

Differentiate both sides with respect to t:\[\bf 3x^2\frac{ dx }{ dt }+3y^2\frac{ dy }{ dt }=0\]Now plug in: dx/dt = -3, x = 1, y = 2:\[\bf 3(1)^2(-3)+3(2)^2\frac{ dy }{ dt }=0\]Now rearrange and solve for dy/dt.

Answer 14

@RyanRyan

Answer 15

@RyanRyan You see what I did there? Do you have any questions/trouble understanding?

Answer 16

yea, 3/4.. thanks guys

Answer 17

@RyanRyan Good job. Your answer is correct =D.