Question

How do you determine the concavity for `g(x)=-x^2+3x+4`?

Answer 1

The concavity of a function is the sign of its second derivative.
If, in a set, it is positive, than the concavity is up, if negative the concavity is down, if it is zero, there could be an inflection point there.

So:

`y'=-2x+3`

`y''=-2`.

Since the second derivative is always negative, it has always concavity dawn.