calculus

posted by .

Consider the curve given by the equation y^3+3x^2y+13=0

a.find dy/dx

b. Write an equation for the line tangent to the curve at the point (2,-1)

c. Find the minimum y-coordinate of any point on the curve.

the work for these would be appreciated i don't need the answers.

  • calculus -

    differentiate implicitly.
    3y^2 dy/dx + 3x^2 dy/dx + 6xy + 0 = 0
    dy/dx(3y^2 + 3x^2) = -6xy
    dy/dx/ = -6xy/(3y^2 + 3x^2)

    b) sub in x = 2, to get the slope, then use the grade 9 way to find the equation of a line given the slope and a point.

    c) set dy/dx = 0
    so -6xy = 0
    x = 0 or y = 0
    when x = 0, y^3 +1 = -13
    y = (-13)^(1/3) = appr. - 2.35

    when y = 0, 0 + 0 + 13 = 0 , not possible.
    so we have one turning point at (0,-2.35)

    what about when x becomes large either + or -
    investigate for x = 100
    y^3 + 30000y = -13
    y = -13/30000 which approaches zero.
    the same thing is true if x = -100

    so the minimum value of y is -2.35 when x = 0

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    the curve: (x)(y^2)-(x^3)(y)=6 (dy/dx)=(3(x^2)y-(y^2))/(2xy-(x^3)) a) find all points on the curve whose x-coordinate is 1 and write an equation for the tangent line of each of these points b)find the x-coordinate of each point on …
  2. calculus

    Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2 + 1 and connect the tangent point to the x-axis. If the tangent point is close to the y-axis, the line segment is long. If the tangent …
  3. 12th Grade Calculus

    1. a.) Find an equation for the line perpendicular to the tangent curve y=x^3 - 9x + 5 at the point (3,5) [* for a. the answer that I obtained was y-5 = -1/18 (x-3) ] b.) What is the smallest slope on the curve?
  4. AP Calculus

    Consider the curve given by x^2+4y^2=7+3xy a) Show that dy/dx=(3y-2x)/(8y-3x) b) Show that there is a point P with x-coordinate 3 at which the line tangent to the curve at P is horizontal. Find the y-coordinate of P. c) Find the value …
  5. calculus

    1. Given the curve a. Find an expression for the slope of the curve at any point (x, y) on the curve. b. Write an equation for the line tangent to the curve at the point (2, 1) c. Find the coordinates of all other points on this curve …
  6. Calculus

    Consider the curve -8x^2+5xy+y^3=-149 1. Find Dy/dx 2. write an equation for the line tangent to the curve at the point (4,-1)
  7. calculus

    Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show that dy/dx= (4x-2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope -1 is tangent to the curve …
  8. Calculus

    Please help this is due tomorrow and I don't know how to Ive missed a lot of school sick Consider the curve given by the equation x^3+3xy^2+y^3=1 a.Find dy/dx b. Write an equation for the tangent line to the curve when x = 0. c. Write …
  9. AP AB Calculus

    Linear approximation: Consider the curve defined by -8x^2 + 5xy + y^3 = -149 a. find dy/dx b. write an equation for the tangent line to the curve at the point (4,-1) c. There is a number k so that the point (4.2,k) is on the curve. …
  10. Calculus AB

    Could someone please help me with these tangent line problems?

More Similar Questions