The given following function $f(x) = ax + b$ is strictly increasing for all real $x$ if $\ A) a > 0 \\ B) a < 0 \\ C) a = 0 \\ D) a \leqslant 0 \\ \ $
Hint: Suppose that a function y=f(x) is a differentiable function. In order for the function to be strictly increasing it is necessary and sufficient that it has to follow a condition where $f'(x) > 0$.
Here the given function is $f(x) = ax + b$.
To find the condition for given increasing function we have to find $f'(x)$ So, if we differentiate the given function $f(x)$ with respective $x$ we get $f(x) = ax + b$ $f'\left( x \right) = a$
We know that for any increasing function $f'(x)$ should be greater than zero i.e. $f'(x) > 0$. From the given function we can say that $f'\left( x \right) = a$ So from this we can say that for the given function $f(x) = ax + b$ is strictly increasing function for all real x when$a > 0$, where$f'\left( x \right) = a$.