Question

How do you determine the intervals where `f(x)=x^2-4x+7` is concave up or down?

Answer 1

See below.

Explanation:

Answer 1

The graph of `f` is a parabola (because `f` is a quadratic function) that opens upward (because `a` is positive). So it is concave up everywhere.

Answer 2

`f''(x) = 2` is positive everywhere, so the graph of `f` is concave up everywhere.