Posted by **Jessica Chaney** on Thursday, March 1, 2012 at 1:13pm.

Please help this is due tomorrow and I dont 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 an equation for the normal line to the curve when x = 0.

d. Find all the points on the curve where the curve has a horizontal or vertical tangent.

- Calculus -
**Steve**, Thursday, March 1, 2012 at 3:55pm
x^3+3xy^2+y^3=1

3x^2 + 3y^2 + 6xyy' + 3y^2 y' = 0

y' = -(x^2+y^2)/(2xy + y^2)

when x=0, y=1

y'(0) = -(0+1)/(0+1) = -1

tangent line at (0,1) is y=-x+1

slope of normal = 1

line is y=x+1

only place where tangent could be horizontal (y'=0) would be at (0,0) but that point is not on the graph.

Vertical tangents where 2xy+y^2 = 0

at y=0 x=1

y' = -1/0 -- vertical tangent

y(2x+y) = 0

y = -2x

y' = -(x^2 + 4x^2)/(2x(-2x) + 4x^2) = -5x^2/0 -- vertical tangent

when y=-2x,

x^3+3xy^2+y^3=1

x^3 + 3x(4x^2) - 8x^3 = 1

x^3 + 12x^3 - 8x^3 = 1

5x^3 = 1

x = 0.5848

so, vertical tangent at (.5848,-1.1696)

## Answer this Question

## Related Questions

- calculus - Consider the curve given by the equation y^3+3x^2y+13=0 a.find dy/dx...
- Calculus - what is the curve given by the equation x^3=3xy^2+y^3=1 what is dy/dx...
- Calculus - 2y^3 - 3xy = 4 1) Find dy/dx 2) Write an equation for the line ...
- AP AB Calculus - Linear approximation: Consider the curve defined by -8x^2 + 5xy...
- Calculus - Consider the curve -8x^2+5xy+y^3=-149 1. Find Dy/dx 2. write an ...
- Calculus - Find the equation of the tangent line to the curve x^(3)+3xy+y^(3)=1 ...
- Calculus - Can someone show how this question is solved. Consider the curve ...
- calculus - 1. Given the curve a. Find an expression for the slope of the curve ...
- AP Calculus - Consider the curve given by x^2+4y^2=7+3xy a) Show that dy/dx=(3y-...
- calculus - what is the equation of the tangent line to the curve x^3 + 2y^2 + ...

More Related Questions