calculus

posted by Taeyeon

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. Reiny

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)

2. Taeyeon

This is what I found in the paper though.

3. Anonymous

\$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

Similar Questions

1. math

consider the curve defined by the equation y=a(x^2)+bx+c. Take a point(h,k) on the curve. use Wallis's method of tangents to show that the slope of the line tangent to this curve at the point(h,k) will be m= 2ah+b. have to prove this …
2. Help Calc.!

original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point …

original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point …
4. Need help fast on calc

original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point …
5. Calculus

Please help this is due tomorrow and I don't know how to Ive missed a lot of school sick Consider the curve given by the equation x^3+3xy^2+y^3=1 a.Find dy/dx b. Write an equation for the tangent line to the curve when x = 0. c. Write …
6. Calculus [finding slope of tangent line]

Find the slope of the tangent line to the curve 0x^2−2xy+2y^3=10 at point (-4,1) Help please?
7. 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 tangent …
8. AP AB Calculus

Linear approximation: Consider the curve defined by -8x^2 + 5xy + y^3 = -149 a. find dy/dx b. write an equation for the tangent line to the curve at the point (4,-1) c. There is a number k so that the point (4.2,k) is on the curve. …
9. Calculus AB

Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive?