Question

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

Answer 1

f(x) = (ax+b)(x^2 -5x + 4)^-1
f = ax + b
f' = a
g = (x^2 - 5x + 4)^-1
g' = -1(x^2 - 5x + 4)^-2(2x - 5)

Answer 2

Is this correct?

Answer 3

I am going to carry on using the product rule..