Calculus

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=?

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  1. 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.

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