Calc

Line L is tangent to the graph of y= x- (x^2/500) at the point Q
a) find the x coordinate of point Q
B) right an equation for line L
C) suppose the graph above were a hill (measured in feet). There is a 50 foot tree growing vertically at the top of the hill. Does a spot light (a point P, on the x axis along the line L) shine on any part of the tree?

  1. 👍 0
  2. 👎 0
  3. 👁 1,270
  1. Did you want that tangent to be horizontal ?
    if so, then

    dy/dx = 1 - x/250

    to be horizontal tangent, dy/dx = 0
    x/250 = 1
    x = 250
    then y = 250 - (250^2)/500 = 125
    Q is (250,125)

    b) Did you mean" write" an equation for line L ?

    Until you clarify your question, I will stop here.

    1. 👍 0
    2. 👎 2
  2. they drew a diagram for it and Q is actually on the left side of the graph making the line L an upward slant, and yes i meant "write"

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. Find the x coordinate of the point where the tangent line is parallel to the

  2. Calculus

    1. use the definition mtan=(f(x)-f(x))/(x-a) to find the SLOPE of the line tangent to the graph of f at P. 2. Determine an equation of the tangent line at P. 3. Given 1 & 2, how would I plot the graph of f and the tangent line at

  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

  4. Calculus

    Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2), with x ≠ 2. a.Find all values of x where the graph of g has a critical value. b.For each critical

  1. Math

    At what point on the graph of y=(1/2)x^2-(3/2) is the tangent line parallel to the line 4x-8y=5? A. (1/2,-3/8) B. (1/2,-11/8) C. (2,3/8) D. (2,1/2) E. (-1/2,-11/8)

  2. 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

  3. Calculus

    Graph the function f(x)=x+4/x Graph the secant line that passes through the points (1,5) and (8,8.5) on the same set of axes Find the number c that satisfies the conclusion of the Mean Value Theorem for f on [1,8] c= Notice that

  4. math

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x)=7x-5x^2 at (-2,-34) m = ?? y = ?? .

  1. calculus

    Find an equation of the tangent line to the graph at the given point. (The graph is called a Witch of Agnesi.) f(x)= 7 / x^2 + 3 (2,1)

  2. Calculus

    1. On what interval is the function f(x)=x^3-4x^2+5x concave upward? 2. For what values of x dies the graph of f(x)=2x^3-3x^2-6x+87 have a horizontal tangent? Is there no solution because the equation can't be factored? 3. At what

  3. Calc

    Write the equation of the line tangent to the graph of the function at the indicated point. As a check, graph both the function and the tangent line you found to see whether it looks correct. (1/x^3 -x)^2 at x= 2

  4. calculus

    find the x coordinate of each point at which the line tangent to the graph of f(x)=x^4-3x^2 is parallel to the line y= -2x+4

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