Question

For A level syllabus, function chapter. Well, what does it mean increasing function? Like when I'm trying to solve past year, there is one question about explain why the equation is an increasing function. I differentiate and get the new equation. I got x= in negative value, so is it still consider as an increasing function? I'm confused. Tq

Answer 1

An equation is a increasing function if f'(x) is strictly positive for all values of x. If you plug in a value and f'(x) yields a positive number, then the function is increasing for that value of x.

The same applies for decreasing functions.

Answer 2

Get it, u r right ! Tq

Answer 3

Sometimes a distinction is made between increasing function \(f'(x)\ge0 ~\forall x\in domain\)

and strictly increasing function
\(f'(x)\gt0 ~\forall x\in domain\)