Calculus

posted by .

An isosceles triangle, whose base is the interval from (0,0) to (c,0), has its vertex on the graph of f(x)=12-x^2. For what value of c does the triangle have maximum area?

  • Calculus -

    Let A(a,12-a^2) be the point of the triangle which lies on the parabola.
    Since it must be an isosceles triangle, c = 2a

    The area of the triangel = 1/2(c)(12-a^2)
    =1/2(2a)(12-a^2)
    =12a - a^3

    Then d(Area)/da = 12 - 3a^2
    = 0 for a max area

    3a^2 = 12
    a = +- 2, c = 2a
    so c = 4

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. corollary to isosceles triangle theorem

    how to prove 1)the measure of each angle of an equilateral triangle is 60. 2)the bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. Thanks. 1) The angles in any triangle have to add up …
  2. Calculus

    An isosceles triangle has a vertex at the origin. Determine the area of the largest such triangle that is bound by the function x^2 + 6y = 48. So, y=8 when x=0 making a vertical side equal to 8. I also determined that there is a zero …
  3. calculus

    An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x-axis. The vertices of the base are on the curve 5y=25-x^2 Find the area of the largest such triangle.
  4. math

    9. An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x-axis. The vertices of the base are on the curve Find the area of the largest such triangle.
  5. Calculus

    A right triangle has one leg on the x-axis. The vertex at the right end of that leg is at the point (3,0). The other vertex touches the graph os y=e^x. the entire triangle is to lie in the first quadrant. Find the maximum area of this …
  6. math

    an isosceles triangle has a vertex at the origin. Determine the area of the largest such triangle that is bound by the function x squared + 6y = 48 and explain why this is infact the maximum area.
  7. calculus

    5. Let for and f(x)=12X^2 for x>=0 and f(x)>=0 a. The line tangent to the graph of f at the point (k, f(k)) intercepts the x-axis at x = 4. What is the value of k?
  8. Math

    An isosceles triangle has its vertex at the origin and the ends of its base on the parabola y=9-x^2. Express the area of the triangle as a function of the length of its base. Assume its base lies above the x-axis.
  9. Precalculus

    The sides of an isosceles triangle are 10 cm, 10 cm, and 12 cm. A rectangle is inscribed in the triangle with one side on the triangle's base. The other two vertices of the rectangle are on the triangle's legs. Find the Maximum Area …
  10. Math geometry

    1) The base angles of an isosceles triangle are (50-x)^6 and (30x-12)^6 what is the vertex angle?

More Similar Questions