2. The graph of has a f(x)=(ax+b)/((x-1)(x-4)) horizontal tangent line at (2,-1). Determine the valuesaandb.

Setting f(x) =-1 and subbing in x=2, we get

Sub in x=2 into f'(x), we get

Since the line is horizontal, we have

We have two small equations in 2 unknowns:

Solve for a and b

Sub x=-1 into f(x) and we find y=1

Sub x=-1 into f'(x) to find the slope at x=-1. We get m=-2/3

Use the given coordinates and the new found slope to find the equation of our line:

Therefore, the equation of the line is

Set f(x) and the line equation equal and solve for x: