Cho hàm số f(x)=ax+1/bx-1 có đồ thị (C)

* Hướng dẫn giải

Đáp án C

Ta có $f^{\text{'}}\left(x\right)=\frac{-a-b}{{(b\text{x}-1)}^2}$, khi đó theo đề ra ta có:

$$\begin{gathered} \left\{\begin{array}{l}y=\frac{a}{b}=2\\ f^{\text{'}}\left(1\right)=\frac{-a-b}{{(b-1)}^2}=-6\end{array}\right.\iff \left\{\begin{array}{l}a=2b\\ 6{(\mathrm{b}-1)}^2=a+b\end{array}\right.\iff \left[\begin{array}{l}a=1;b=\frac{1}{2}\\ \left\{\begin{array}{l}a=4\\ b=2\end{array}\right.\end{array}\right.\Rightarrow \left[\begin{array}{l}a-b=\frac{1}{2}\\ a-b=2\end{array}\right. \\ \Rightarrow \max (a-b)=2 \end{gathered}$$.