Question

What would the concavity be if f''(x)=0, since it is neither positive nor negative?

Answer 1

depends on what the sign of f''(x) was before and after f''(x)=0

Answer 2

points where f''(x)=0 are called 'inflection points'
for a function like f(x)=x, where f''=0, it is just said that the concavity is zero

Answer 3

Don't you have to test around the interval where f''(x)=0 to determine if it is an inflection point?

Answer 4

well what is the concavity of x = y
f'(x) = 1
f''(x) = 0

Therefore there is no concavity because it is a line

Answer 5

Dock is right, Turing is half right....you can't say that it's an inflection point just because concavity is 0. There must be a CHANGE in concavity at that point.