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 the correct option

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

We know that a function is always increasing if $f\text{'}\left(x\right)>0$

And,
$\begin{array}{rcl}f\text{'}\left(x\right)& =& \frac{d}{dx}\left(ax+b\right)\\ \therefore f\text{'}\left(x\right)& =& a\end{array}$

Thus, if $a>0$, the function is increasing for all real values of $x$.

Hence, option(A) is correct.