Friday

August 22, 2014

August 22, 2014

Posted by **Anonymous** on Wednesday, March 13, 2013 at 9:12pm.

If x3 + y3 - xy2 = 5, find dy/dx.

(b)

Using your answer to part (a), make a table of approximate y-values of points on the curve near x = 1, y = 2. Include x = 0.96, 0.98, 1, 1.02, 1.04.

(c)

Find the y-value for x = 0.96 by substituting x = 0.96 in the original equation and solving for y using a computer or calculator. Compare with your answer in part (b).

(d)

Find all points where the tangent line is horizontal or vertical.

- calculus -
**Reiny**, Wednesday, March 13, 2013 at 9:26pma) Assuming you meant

x^3 + y^3 - x y^2 = 5

3x^2 + 3y^2 dy/dx - x(2y)dy/dx - y^2 = 0

dy/dx(3y^2 - 2xy) = y^2 - 3x^2

dy/dx = (y^2 - 3x^2)/(3y^2 - 2xy)

b) just arithmetic, you do it

c) yours

d) for a horizontal tangent, dy/dx = 0

then y^2 - 3x^2 = 0

y^2 = 3x^2

y = ± x√3

sub into the first:

x^3 + 3√3x^3 - x(x√3) = 5

x^3 + 3√3 x^3 - √3 x^2 - 5 = 0

Nastiness!!!!

wolfram says x = 1.03412 correct to 5 decimals

now sub that into the original and find y, equally nasty.

for vertical asymptote , denominator of dy/dx = 0

3y^2 - 2xy) = 0

y(3y - 2x) = 0

y = 0 , that is not bad

or

y = 2x/3

more mess ahead

I suggest you use the Wolfram page or your built-in equation solver of your fancy calculator to solve these equations.

(it might be a good idea to check my work, lately I have been making silly errors by not writing out the solution first)

**Related Questions**

calculus - If x^{2} + y^3 - x y^2 = 5, find dy/dx in terms of x and y. Using ...

Calculus (pleas help!!!) - A) If x^2+y^3−xy^2=5, find dy/dx in terms of x ...

Calculus Please Help - A) If x^2+y^3−xy^2=5, find dy/dx in terms of x and...

Calculus - Consider the curve defined by y + cosy = x +1 for 0 =< y =< 2pi...

Maths 2U - how do you find the horizontal and vertical assymptotes of the curve ...

math - Part A: Does the table represent a relation that is a function? Justify ...

math - make a table of values for thsi equation with at least 4 points in each ...

Algebra - x -1 -1 -2 -2 y 0 -1 2 3Part A: Does the table represent a relation ...

Calculus - a)The curve with equation: 2y^3 + y^2 - y^5 = x^4 - 2x^3 + x^2 has ...

12th Grade Calculus - 1. a.) Find an equation for the line perpendicular to the ...