a) 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
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
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
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)
parabolas - how do i find the equaion of the following parabolas? 1)intercepts ...
Math Calculus - This is a problem set I do not undestand Let y1 = a^x, y2 = NDER...
math - If x=1/7+4√3 and y=1/7-4√3, then find the value of (i)x2+y2 (...
Math - Find a polynomial of degree 3 with roots 3, 4 - i. Which one is it? A.x3...
maths - Write the system as a matrix equation and solve using inverses. x1 + 2x2...
Math HELPPPP - (a) Which of the following are examples of the expression "...
physics - Which of the following equations is dimensionally consistent? A. a3 = ...
algebra - Is the LCM for xy, y3 = x3y3, y3
Calculus Assignment - Hey there. Okay well I just started first year university ...
University of Phoenix - Minimize w= y1+y2+4y3 subject to y1+2y2+3y3>=115 2y1+...