Calculus
posted by Ashley .
determine the point(s)at which the graph of y^4 = y^2 x^2 has a horizontal tangent.

Calculus 
Steve
y^4 = y^2  x^2
4y^3 y' = 2y y'  2x
y' = 2x/(4y^32y)
Now, assuming that y ≠ 0 or ±1/√2,
y'=0 when x=0
so, y^4 = y^2, and y = ±1, so
(0,1) and (0,1)
extra credit: what happens at y = 0 or ±1/√2? 
Calculus 
Ashley
how did you know it was + or  l? I got what x equals but I was confused on how to find the y values?

Calculus 
Steve
if x=0,
y^4 = y^2
y^2(y^21) = 0
y = 0 or ±1
but y=0 is not a possibility. 
Calculus 
Ashley
where did you get y^2 1 from? Did you subtract y^2 from the right side? if so where did the 1 come from?

Calculus 
Steve
Hello? This is calculus. Have you forgotten you algebra I?
y^4 = y^2
y^4  y^2 = 0
y^2(y^21) = 0
...
Respond to this Question
Similar Questions

calculus
let f be the function f(x) = x^3 + 3x^2  x + 2 a. the tangent to the graph of f at the point P = (2,8) intersects the graph of f again at the point Q. Find the coordinates of point Q. b. Find the coordinates of point R, the inflection … 
Calculus Help
Determine the point at which the graph of the function has a horizontal tangent line. f(x) = (9x^2)/(x^2+6) 
Calculus  Functions?
#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = 1, and the graph of f has a point of inflection at x= 2 a.) Find the values of a … 
Calculus
Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line for y=(3^1/2)x+2cos(x), 0¡Üx<2¦Ð 
calculus
If a function f is continuous for all x and if f has a relative minimum at (1,4) and a relative minimum at (3,2), which of the following statements must be true? 
Calculusderivatives
Verify these answers~ 1. For what value(s) of x does f(x)=(x^216)^5 have a horizontal tangent? 
cal
Determine all values of x, (if any), at which the graph of the function has a horizontal tangent. y(x) = 6x/(x9)^2 when i workout this problem I get this: by quotient rule: dy/dx = ( (x9)^2 (6)  6x(2)(x9))/(x9)^4 = 0 at a horizontal … 
Calculus
The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(11/x^2)cos(x+1/x). A. Find all values of x in the interval 0.12<=x<=1 at which the graph of g has a horizontal tangent line. B. On what subintervals … 
math (horizontal tangent line)
Determine the point(s) if any at which the graph of the function has a horizontal tangent line. y=x^3+x I graphed this function out and it looks like there isn't any horizontal tangents. Am I correct or am I forgeting something? 
Calculus AB
Could someone please help me with these tangent line problems?