Posted by **Karen** on Monday, August 4, 2014 at 7:37pm.

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 -
**Damon**, Monday, August 4, 2014 at 7:51pm
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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