If f '(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 ______________.

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Solution

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 '(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 '(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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