help! horizontal tangents

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

[math] f(x)=\frac{\mathit{ax}+b}{\left(x-1\right)\left(x-4\right)} [/math]
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?
 
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