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

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Answer 1 · 2016-11-27T13:39:43

See below.

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.

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