Inflection ?

[steel topaz]

do you know the conditions for an inflection point?

and what are the second derivatives like for a concave and convex point

so do you know how the second derivative is the rate of change of gradient?

a concave point looks like this

do you see how the gradient is decreasing?

therefore the second derivative is negative

yeah

?

if you know the second derivative before is negative and it's positive after

what can you assume about the second derivative of the inflection point

since it should be continuous

if something goes from negative to positive

then it must pass through 0 right?

[hazy dagger]

basically the inflection point is where concavity switches

when the second derivative is positive it means that it is concave up (change of rate is increasing and therefore making a U shape)

when it is negative it means that it is concave down

so where the concavity switches it is the inflection point which also means that it is when the second derivative is 0