Stationary points? Inflexion points? Turning points? What's What? (1 Viewer)

[omniscientbeing]

Ok so I know this may be a pretty stupid Q but I'm confused about the difference between stationary, inflexion and turning points. I think inflexion points are where the concavity of a curve changes and that turning points refer to maximum & minimum but when it comes to stationary points I get confused about whether these are when the 1st or 2nd derivative = 0, or both? I dunno I think I'm just confused about all these points and how they relate to each other. Can anyone explain this stuff as simply as possible?

 

[ssglain]

Stationary pts occur at f'(x) = 0. However if also f"(x) = 0 at this pt, in most cases it is no longer a turning pt but instead a horizontal pt of inflexion.

You do need to take care to determine the concavity on either side of a pt for which f"(x) = 0 because for example y = x^4 will have both 1st and 2nd derivative equal to 0 at (0,0) but this is a minimum turning pt not a horizontal pt of inflexion.

I hope that answers your query.

 

[kony]

for hsc maths,

f'(x) = 0 : this means either turning point, or horizontal inflexion point
f''(x) = 0 : this means inflexion (horizontal or oblique)

but as ssglain pointed out, in real life f''(x) = 0 has many cases where it is actually a turning point. (i think it might be because its a vertical inflexion, but that's just a guess)

however as already said, in the hsc, the f''(x) = 0 means inflexion.