Question

The function $f\left(x\right)=ax+b$ is strictly increasing for all real $x$, if

• A. $a>0$
• B. $a<0$
• C. $a=0$
• D. $a\le 0$

Answer 1

The correct option is A

$a>0$

Explanation for correct option

Given function $f\left(x\right)=ax+b$

$\Rightarrow f\text{'}\left(x\right)=a$

We know that for strictly increasing function, $f\text{'}\left(x\right)>0$.

$\Rightarrow a>0$

Thus, $f\left(x\right)$ is strictly increasing for all real $x$ if $a>0$.

Hence, the correct option is $\left(\mathrm{A}\right)$.