Maybe this is a question that is a bit redundant.

I just started the chapter on curve sketching. The first section is about local maxima and minima.

How do I determine the sign of the first derivative to see if it changes at the possible turning point? I know that a function like f(x) = x^3 doesn't have a turning point.

Do I need to start sketching the curve by plotting the possible turning points or is there a more intuitive way to determine if there is a sign change.

thanks