Question:
Without using the derivative show that the function $f(x)=7 x-3$ is strictly increasing function on $R$.
Solution:
Given,
$f(x)=7 x-3$
Lets $\mathrm{x}_{1}, \mathrm{x}_{2} \in \mathrm{R}$ and $\mathrm{x}_{1}>\mathrm{x}_{2}$
$\Rightarrow 7 \mathrm{X}_{1}>7 \mathrm{X}_{2}$
$\Rightarrow 7 \mathrm{X}_{1}-3>7 \mathrm{X}_{2}-3$
$\Rightarrow \mathrm{f}\left(\mathrm{x}_{1}\right)>\mathrm{f}\left(\mathrm{x}_{2}\right)$
$\therefore f(x)$ is strictly increasing on $R$.
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