If $f^{\prime}(x)$ changes its sign from positive to negative as $x$ increases through $c$ in the interval $(c-h, c+h)$, then $x=c$ is a point of____________
First derivative test states that if f '(x) changes sign from positive to negative as x increases through c, then c is a point of local maxima, and f(c) is local maximum value.
Thus, if $f^{\prime}(x)$ changes its sign from positive to negative as $x$ increases through $c$ in the interval $(c-h, c+h)$, then $x=c$ is a point of local maximum.
If $f^{\prime}(x)$ changes its sign from positive to negative as $x$ increases through $c$ in the interval $(c-h, c+h)$, then $x=c$ is a point of __local maximum___.
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