The graph (in black) is f(x). When asked to for the interval of increase/decrease, would it be correct to say that f(x) is increasing for all values of x? However, f(x) appears to plateau at 1.5<x<2.5. I know a point of inflection occurs at (2, f(2)).
If f(x) is increasing for all values of x, how would I begin to sketch the first derivative (I would need an equation since I cannot draw free-hand curves in the program I use)?
The pencil lines indicate a guess: The quadratic first derivative and linear second derivative.
Could anyone please provide clarification?