# calculus

Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 .
a. Show that dy/dx= (4x-2xy)/(x^2+y^2+1)
b. Write an equation of each horizontal tangent line to the curve.
c. The line through the origin with slope -1 is tangent to the curve at point P. Find the x – and y – coordinates of point P.

1. 👍
2. 👎
3. 👁
2y^3 + (6x^2)(y) - 12x^2 + 6y = 1
then your dy/dx is not correct

I get:
8y^2 dy/dx + 6x^2 dy/dx + 12xy - 24x + 6dy/dx = 0
dy/dx(8y^2 + 6x^2 + 6) = 24x - 12xy
dy/dx = 12x(2 - y)/(2(4y^2 + 3x^2 + 3) )
= 6x(2-y)/(4y^2 + 3x^2 + 3)

1. 👍
2. 👎
2. This is what I found in the paper though.

1. 👍
2. 👎
3. \$4000 is invested at 9% compounded quarterly. In how many years will the account have grown to \$14,500? Round your answer to the nearest tenth of a year

1. 👍
2. 👎

## Similar Questions

1. ### calculus

1. If 3x^2+2xy+y2=2 then the value of dy/dx x = 1 is A. -2 B. 0 C. 2 D. 4 E. not defined

2. ### Calculus!! HELP!!

1) The sides of the triangle shown increase in such a way that (dz/dt=1) and (dx/dt=(3dy/dx)) At the instant when x = 12 and y = 5, what is the value of dx/dt? 2) Let f(x) = x^3 − 4. Which of these is the equation for the normal

3. ### Calculus

The line that is normal to the curve x^2=2xy-3y^2=0 at(1,1) intersects the curve at what other point? Please help. Thanks in advance. We have x2=2xy - 3y2 = 0 Are there supposed to be 2 equal signs in this expression or is it x2 +

4. ### Calculus

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

Use implicit differentiation to find the points where the parabola defined by x^{2}-2xy+y^{2}-6x+2y+17 = 0 has horizontal and vertical tangent lines. List your answers as points in the form (a,b).

2. ### math

A curve has implicit equation x^2-2xy+4y^2=12 a)find the expression for dy/dx in terms of y and x. hence determine the coordinates of the point where the tangents to the curve are parallel to the x-axis. b)Find the equation of the

3. ### Maths

Consider the curve defined by y4= y2- x2. At what ordered pair (x,y) is the line 4x√3-4y=1 tangent to the curve y4= y2- x2?

4. ### Calculus

A curve is defined by the parametric equations: x = t2 – t and y = t3 – 3t Find the coordinates of the point(s) on the curve for which the normal to the curve is parallel to the y-axis. You must use calculus and clearly show

1. ### math

For the curve given by 4x^2+y^2=48+2xy, show that there is a point P with x-coordinate 2 at which the line tangent to the curve at P is horizontal.

2. ### Calculus

Consider the equation: x^2 - 2xy + 4y^2 = 64 Write an expression of the slope of the curve at any point. (y^p)= y prime My work 2x - 2(xy^p + y) + 8yy^p = 0 2x -2xy^p - 2y + 8yy^p = 0 -2xy^p + 8yy^p = 2y -2x factored out y^p and

3. ### math

Lana uses factoring by grouping to factor the polynomial 8x2y−10xy2+12x−15y. Her work is shown below, but the last two lines of work are missing. 8x2y−10xy2+12x−15y (8x2y−10xy2)+(12x−15y) __[blank 1]__ __[blank 2]__

4. ### Calculus

Consider the closed curve in the day plane: 2x^2-2xy+y^3=14 a) show that dy/dx=2y-4x/3y^2-2x (I got this part) b) find equation lines to the curve when y=2 c) if the point (2.5, k) is on the curve, use part b to find the best