# Free response question help

• Feb 12th 2010, 06:36 AM
wisezeta
Free response question help
I would appreciate some help with this problem, I have some ideas how to approach it but I'm confused on what to do on some parts.

Consider the curve given by y^2= 2+xy

1) show that dy/dx= y/2y-x (im pretty sure i can do this if its just the derivative)

2) find all points (x,y) on the curve where the line tangent to the curve has slope 1/2 (how do u find a tangent line with a specific slope, and how would you get the points)

3) show that there are no points (x,y) on the curve where the line tangent to the curve is horizontal (this isn't horizontal asymptote right?)

4) let x and y be functions of time t that are related by the equation y^2= 2+xy. At time t=5, the value of y is 3 and dy/dt= 6. Find the value of dx/dt at time t=5 (where exactly does t go in that equation and how do i apply it?)
• Feb 12th 2010, 06:51 AM
dedust
Quote:

Originally Posted by wisezeta
I would appreciate some help with this problem, I have some ideas how to approach it but I'm confused on what to do on some parts.

Consider the curve given by y^2= 2+xy

1) show that dy/dx= y/2y-x (im pretty sure i can do this if its just the derivative)

2) find all points (x,y) on the curve where the line tangent to the curve has slope 1/2 (how do u find a tangent line with a specific slope, and how would you get the points)

3) show that there are no points (x,y) on the curve where the line tangent to the curve is horizontal (this isn't horizontal asymptote right?)

4) let x and y be functions of time t that are related by the equation y^2= 2+xy. At time t=5, the value of y is 3 and dy/dt= 6. Find the value of dx/dt at time t=5 (where exactly does t go in that equation and how do i apply it?)

2) slope $= m = \frac{dy}{dx}$. find all point that satisfy $\frac{dy}{dx} = 0.5$

3) show that there is no point satisfy $\frac{dy}{dx} = 0$

4) use implicit differentiation with respect to $t$
• Feb 12th 2010, 07:15 AM
wisezeta
i don't understand how to do the implicit differentiation for t
• Feb 12th 2010, 10:34 AM
skeeter
Quote:

Originally Posted by wisezeta
i don't understand how to do the implicit differentiation for t

$\frac{d}{dt}[y^2 = 2+xy]$

$2y \cdot \frac{dy}{dt} = x \cdot \frac{dy}{dt} + y \cdot \frac{dx}{dt}$
• Feb 12th 2010, 01:17 PM
wisezeta
so what happens to t=5?
• Feb 12th 2010, 01:45 PM
skeeter
Quote:

Originally Posted by wisezeta
so what happens to t=5?

Quote:

let x and y be functions of time t that are related by the equation y^2= 2+xy. At time t=5, the value of y is 3 and dy/dt= 6. Find the value of dx/dt at time t=5
they told you that at time t = 5, y = 3 and dy/dt = 6.

you have enough information to find dx/dt.

(the t = 5 is inconsequential)
• Feb 12th 2010, 01:47 PM
wisezeta
Ok I understand now. Thank you very much
• Feb 15th 2010, 09:50 AM
wisezeta
Quick question, for 2 and 3 do I set the derivative equal to the given number, and if so don't I need a second equation in order to get the points? Would that be the original equation?
• Feb 15th 2010, 04:42 PM
skeeter
yes and yes.