help! horizontal tangents

[danielle trottier]

f(x) = ax+b / (x-1) (x-4)
has horizontal tangent at (2,-1)
must find a & b!!

 

[Cubist]

Hi, welcome to the forum! I assume your picture is correct

$$f(x)=\frac{\mathit{ax}+b}{\left(x-1\right)\left(x-4\right)}$$
so your text equation needed some extra parenthesis: f(x)=(ax+b) / ( (x-1)*(x-4) )

Given that the curve has a horizontal tangent at (2,-1), can you say anything about the value of f(2) ? And does this statement also give any information about the derivative of f(x) at any points?

 

[bduda]