Posted by **Ashley** on Monday, October 1, 2012 at 3:00pm.

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

- Calculus -
**Steve**, Monday, October 1, 2012 at 3:12pm
y^4 = y^2 - x^2

4y^3 y' = 2y y' - 2x

y' = -2x/(4y^3-2y)

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**, Monday, October 1, 2012 at 3:27pm
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**, Monday, October 1, 2012 at 3:29pm
if x=0,

y^4 = y^2

y^2(y^2-1) = 0

y = 0 or ±1

but y=0 is not a possibility.

- Calculus -
**Ashley**, Monday, October 1, 2012 at 3:43pm
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**, Monday, October 1, 2012 at 4:16pm
Hello? This is calculus. Have you forgotten you algebra I?

y^4 = y^2

y^4 - y^2 = 0

y^2(y^2-1) = 0

...

## Answer This Question

## Related Questions

- Calculus Help - Determine the point at which the graph of the function has a ...
- Calculus - Determine the point(s) (if any) at which the graph of the function ...
- calculus - let f be the function f(x) = x^3 + 3x^2 - x + 2 a. the tangent to the...
- cal - Determine all values of x, (if any), at which the graph of the function ...
- Calculus AB - Could someone please help me with these tangent line problems? 1) ...
- Calculus - Functions? - #1. A cubic polynomial function f is defined by f(x) = ...
- calculus - If a function f is continuous for all x and if f has a relative ...
- Calculus - The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), ...
- Calculus-derivatives - Verify these answers~ 1. For what value(s) of x does f(x...
- math (horizontal tangent line) - Determine the point(s) if any at which the ...

More Related Questions