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concavity

Which way a curve bends — up like a cup ( $f''>0$ ) or down like a frown ( $f''<0$ ).

$f$ is concave up on an interval where $f''>0$ (the graph bends upward, tangent lines lie below the curve) and concave down where $f''<0$ (tangent lines lie above the curve).

Examples

$f(x)=x^2$ is concave up everywhere ( $f''''=2>0$ ); $f(x)=-x^2$ is concave down everywhere.

See also

higher-order derivative inflection point

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Graph settings

indep dep deg

grid intersections

xmin xmax ymin ymax

x-tick y-tick

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