IMathAS-libretexts

Match each statement with its correct completion.

$\displaystyle {f{{\left({x}\right)}}}$ has a local minimum at $\displaystyle {x}={a}$ if
$\displaystyle {f{{\left({x}\right)}}}$ has a global maximum at $\displaystyle {x}={a}$ if
$\displaystyle {f{{\left({x}\right)}}}$ has a global minimum at $\displaystyle {x}={a}$ if
$\displaystyle {f{{\left({x}\right)}}}$ has a local maximum at $\displaystyle {x}={a}$ if
$\displaystyle {f{{\left({x}\right)}}}$ has a local extrema at $\displaystyle {x}={a}$
$\displaystyle {f{{\left({x}\right)}}}$ has a global extrema at $\displaystyle {x}={a}$ if

$\displaystyle {f{{\left({a}\right)}}}\geq{f{{\left({x}\right)}}}$ for all $\displaystyle {x}$ near $\displaystyle {a}$ .
$\displaystyle {f{{\left({a}\right)}}}$ is a local maximum or minimum.
$\displaystyle {f{{\left({a}\right)}}}\leq{f{{\left({x}\right)}}}$ for all $\displaystyle {x}$ in the domain of $\displaystyle {f{{\left({x}\right)}}}$ .
$\displaystyle {f{{\left({a}\right)}}}\geq{f{{\left({x}\right)}}}$ for all $\displaystyle {x}$ in the domain of $\displaystyle {f{{\left({x}\right)}}}$ .
$\displaystyle {f{{\left({a}\right)}}}$ is a global maximum or minimum.
$\displaystyle {f{{\left({a}\right)}}}\leq{f{{\left({x}\right)}}}$ for all $\displaystyle {x}$ near $\displaystyle {a}$ .