Friday

August 22, 2014

August 22, 2014

Posted by **Mathew** on Wednesday, October 2, 2013 at 9:36pm.

(a) show that dy/dx= y/(2y-x)

(b) Find all points (x,y) on the curve where the line tangent to the curve has slope 1/2.

(c) Show that there are now points (x,y) on the curve where the line tangent to the curve is horizontal.

(d) 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.

I was able to do part A, that was easy, but then with the rest of the parts I didn't know where to start. I know I should plug in 1/2 for the slope and solve but I have two variables of x and y. How should I go about solving these problems?

- Calculus -
**Graham**, Wednesday, October 2, 2013 at 10:39pm(B) You have two simultaneous equations in two variables. The original equation, and the derivative for specified values of dy/dx.

When dy/dx=1/2 :

1/2 = y/(2y-x)

Rearrange:

2y - x = 2y

Hence: x = 0

Substitute back into y^{2}= 2 + xy:

Therefore: y = ±√2

Answer: (0, -√2), and (0, +√2)

**Related Questions**

Calculus - Consider the curve y^2+xy+x^2=15. What is dy/dx? Find the two points ...

Calculus - Please help this is due tomorrow and I dont know how to Ive missed a ...

Calculus - If the equation of the tangent line to the curve: xy^3+xy=6, (3,1) ...

Calculus - Use implicit differentiation to find an equation of the tangent line ...

12th grade calculus - find the lines that are (a) tangent and (b) normal to the ...

Calculus - 3) Consider rectangles located as shown in the first quadrant and ...

calculus - Consider the curve given by the equation y^3+3x^2y+13=0 a.find dy/dx...

Pure Mathematics - 1. Given that the straight line y=c-3x does not intersect the...

Calculus ap - Use implicit differentiation to find the slope of the tangent line...

Calculus - Given x+xy+2y^2=6 find the coordinates of all other points on this ...