sketching graphs using derivatives (1 Viewer)

[NexusRich]

Is it possible to quickly predict the rough shape of these graphs without finding the derivatives? or are there no tricks to curve sketching?

 

[Trebla]

You would have previously learnt how to do stuff like addition/multiplication of ordinates to sketch graphs.

 

[tito981]

for the composite functions, you can consider points which are known either to be intercepts of have gradients of zero through asymptotic behaviors and just sub in those y values to find certain points. From there you can predict a rough shape more easily.

for the curves with multiple functions added/subtracted, you can consider: the domains of the functions present, known intercepts and known asymptotic behaviors.