Calculus

posted by Ashley

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

  1. Steve

    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?

  2. 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?

  3. Steve

    if x=0,

    y^4 = y^2
    y^2(y^2-1) = 0
    y = 0 or ±1
    but y=0 is not a possibility.

  4. 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?

  5. Steve

    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
    ...

Respond to this Question

First Name

Your Answer

Similar Questions

  1. 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 …
  2. Calculus Help

    Determine the point at which the graph of the function has a horizontal tangent line. f(x) = (9x^2)/(x^2+6)
  3. 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 …
  4. 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
  5. 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?
  6. Calculus-derivatives

    Verify these answers~ 1. For what value(s) of x does f(x)=(x^2-16)^5 have a horizontal tangent?
  7. cal

    Determine all values of x, (if any), at which the graph of the function has a horizontal tangent. y(x) = 6x/(x-9)^2 when i workout this problem I get this: by quotient rule: dy/dx = ( (x-9)^2 (6) - 6x(2)(x-9))/(x-9)^4 = 0 at a horizontal …
  8. Calculus

    The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(1-1/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 …
  9. 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?
  10. Calculus AB

    Could someone please help me with these tangent line problems?

More Similar Questions