Question

How do you determine whether the function `g(x)=-x^2+3x+4` is concave up or concave down?

Answer 1

Two methods:

Explanation:

Using calculus, to determine concavity, investigate the sign of the second derivative.

`g(x) = -x^2+3x+4`

`g'(x) = -2x+3`

`g''(x) = -2`

Since `g''(x)` is always negative, the graph of `g` is concave down on the domain of `g`.
Which is to say: `g` is concave down on `(-oo, oo)`.

Using algebra, the graph of this quadratic is a parabola. Since the coefficient of `x^2` is negative, the parabola opens downward. It is concave down.