Thursday

October 23, 2014

October 23, 2014

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

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 3:55pmx^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...

AP Calculus - Consider the curve given by x^2+4y^2=7+3xy a) Show that dy/dx=(3y-...

calculus - Consider curve given by x^2+ 4y^2= 7 + 3xy.. Three part question A) ...

Calculus AP need help! - i dont know how or what to starts Find the slope of the...

Calculus - Find the equation of the tangent line to the curve x^(3)+3xy+y^(3)=1 ...

Calculus - 2y^3 - 3xy = 4 1) Find dy/dx 2) Write an equation for the line ...

physics - A swimmer is capable of swimming 0.45 m/s in still water. (a) If she ...

Calculus - I'm extremely confused on what to do in part a of this question. ...

calculus - what is the equation of the tangent line to the curve x^3 + 2y^2 + ...