If f '(x) changes its sign from negative to positive as x increases t

Question:

If '(x) changes its sign from negative to positive as x increases through c in the interval (c − h, c + h), then = c is a point of ______________.

Solution:

First derivative test states that if '(x) changes sign from negative to positive as x increases through c, then c is a point of local minima, and f(c) is local minimum value.

Thus, if '(x) changes its sign from negative to positive as x increases through c in the interval (c − h, c + h), then = c is a point of local minimum.

If '(x) changes its sign from negative to positive as x increases through c in the interval (c − h, c + h), then = c is a point of ___local minimum___.

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