$$\color{rgb(255,102,102)}y=\frac{1}{x}$$

$$\color{rgb(127,0,0)} \begin{array}{l} {a<b } \\ {\frac{1}{a }>\frac{1}{b}} \end{array}$$

$$\color{rgb(0,0,255)}\Rightarrow \text{Variations sur }]0;+\infty[$$

$$\color{rgb(0,0,255)}\Rightarrow \text{Variations sur }]-\infty;0[$$

$$\color{rgb(0,0,255)}\frac{1}{a}$$

$$\color{rgb(0,0,255)}\frac{1}{b}$$

$$\color{rgb(0,0,255)}a$$

$$\color{rgb(0,0,255)}b$$