Math

The line has equation y=2x+c and a curve has equation y=8-2x-x^2.
1) for the case where the line is a tangent to the curve, find the value of the constant c.
2) For the case where c = 11, find the x-coordinates of the points of intersection of the line and the curve. Find also, by integration, the area of region between the line and the curve.

  1. 👍 0
  2. 👎 0
  3. 👁 650
  1. to solve:
    2x+c = 8-2x-x^2
    x^2 + 4x + c-8 = 0
    to have y = 2x+c to be a tangent, there can be only one real root of the quadratic

    so b^2 - 4ac = 0
    16 - 4(1)(c-8) = 0
    16 - 4c + 32 = 0
    4c = 48
    c = 48/4 = 12

    check with Wolfram:
    http://www.wolframalpha.com/input/?i=y%3D2x%2B12,+y%3D8-2x-x%5E2

    for your second part
    y = 2x+11, y = 8-2x - x^2

    I will let you solve it to show:
    http://www.wolframalpha.com/input/?i=y%3D2x%2B11,+y%3D8-2x-x%5E2

    so for the area:
    A = ∫ (8-2x-x^2 - 2x - 11) dx from -3 to -1
    simplify and finish it

    this looks very straightforward, I trust you can handle it

    1. 👍 1
    2. 👎 0
  2. -1

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    The line that is normal to the curve x^2=2xy-3y^2=0 at(1,1) intersects the curve at what other point? Please help. Thanks in advance. We have x2=2xy - 3y2 = 0 Are there supposed to be 2 equal signs in this expression or is it x2 +

  2. Calculus 1

    The curve y = |x|/(sqrt(5- x^2)) is called a bullet-nose curve. Find an equation of the tangent line to this curve at the point (2, 2)

  3. calculus

    -find the equation of the tangent line to the curve y=5xcosx at the point (pi,-5pi) -the equation of this tangent line can be written in the form y=mx+b where m= and b= -what is the answer to m and b?

  4. Calculus

    The curve y = x/(1 + x^2) is called a serpentine. Find an equation of the tangent line to this curve at the point(2, 0.40).(Round the slope and y-intercept to two decimal places.)

  1. 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

  2. calculus

    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

  3. Calculus

    Consider the curve given by y^2 = 2+xy (a) show that dy/dx= y/(2y-x) (b) Find all points (x,y) on the curve where the line tangent to the curve has slope 1/2. (c) Show that there are now points (x,y) on the curve where the line

  4. Calculus 1

    The curve with the equation y^2=5x^4-x^2 is called a kampyle of Eudoxus. Find an equation of the tangent line to this curve at the point (-1,2).

  1. calculus

    The curve below is called a witch of Maria Agnesi. Find an equation of the tangent line to this curve at the point (-2, 1/5). y=1/(1+x^2)

  2. Calculus

    The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (2, 1) is a point on the curve?

  3. Calculus

    A) The point p(3,1) lies on the curve y= square root x-2. If Q is the point (x, square root x-2) use your calculator to find the slope of the decant line PQ for the following values of x 1) 2.5 2.) 2.9 3.) 2.99 4.) 2.999 5.) 3.5

  4. I would like to understand my calc homework:/

    Consider the differential equation given by dy/dx=(xy)/(2) A) sketch a slope field (I already did this) B) let f be the function that satisfies the given fifferential equation for the tangent line to the curve y=f(x) through the

You can view more similar questions or ask a new question.