the graph of y= (ax+b)/(x-1)(x-4) has a horizontal tangent at the point (2,-1. Find a ANd B.

Question

Please help I have ne idea where to start

Answer 1

Assuming you meant

y= (ax+b)/((x-1)(x-4))
y' = (ax^2+2bx-(4a+5b))/((x-1)(x-4))^2

Now, y'=0 when ax^2+2bx-(4a+5b) = 0
when x=2, that means
4a+4b-4a-5b=0
b=0

So, y = ax/((x-1)(x-4))
at x=2, y=-1, so

2a/-2 = -1
a = 1
and so

y = x/((x-1)(x-4))