Find an equation of the tangent line to the graph of f at the given point.

Question

Find an equation of the tangent line to the graph of f at the given point.

F(X) = x+6/x-1 ( 1/2-13)

y=__?

Answer 1

y=24x -25 is the tangent line through the given point

f(x) = (x+6)/(x-1)

f'(x) = (2x+5)/(x-1)^2

f'(1/2) = 24

y = 24x + b

-13 = 24(1/2) + b

b = -13-12 = -25

y = 24x -25