Calculus

posted by .

Find an equation of the tangent line to the graph of the function f through the point (x0, y0) not on the graph. To find the point of tangency (x, y) on the graph of f, solve the following equation of f '(x).
f '(x) = y0 − y/x0 − x
f(x) = √x
(x0, y0) = (-16, 0)

y=?

  • Calculus -

    y = x^.5

    y' = .5 x^-.5

    sketching this I am going to reverse slope equation

    y' at tangent = m = (y-yo) /( x-xo) = .5x^-.5

    y' = m = (y-0)/(x+16) = .5 x^-.5

    x^.5 /(x+16) = .5 x^-.5

    x/(x+16) = .5
    x = .5 x + 8
    .5 x = 8
    x = 16
    so the tangent hits the curve at x = 16
    where y = 4 so at
    (16,4)
    so this line goes through
    (-16,0) and (16,4)
    You can take it from there I am sure.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    The function f is defined by f(x) = x^3 - x^2 - 4x + 4 The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0, -8) which is not on the graph of f. Find the values of a and b. I have …
  2. calc

    The function f is defined by f(x) = x^3 - x^2 - 4x + 4 The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0, -8) which is not on the graph of f. Find the values of a and b. I have …
  3. Math--Calculus

    Let y = f(x) be the continuous function that satisfies the equation x^4 - (5x^2)(y^2) + 4y^4 = 0 and whose graph contains the points (2,1) and (2,2). Let L be the line tangent to the graph of f at x = 2. (a) Find and expression for …
  4. Math- calculus

    Given f(x) = x ^ 3 - x ^ 2 -4x +4 Find the zeros of f. Write an equation of the line tangent to the graph of f at x = -1 The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0,-8) …
  5. 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 …
  6. cal

    find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8 find the equation of the tangent lines at x=1 and x=-2 graph …
  7. Calculus

    1. Given the function f defined by f(x) = x^3-x^2-4X+4 a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. The point (a, b) is on the graph of f and the line tangent to the graph at (a, b) …
  8. Calculus

    find an equation of the tangent line to the graph of the function f through the point (xsub0, ysub0) not on the graph. TO find the point of tangency (x,y) on the graph of f, solve the equation ....
  9. calculus

    1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?
  10. 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 …

More Similar Questions