(T) or false (F). (1)If f \'(c) = 0, then f has a local maximum or minimum at c.

Question

(T) or false (F). (1)If f '(c) = 0, then f has a local maximum or minimum at c. (2). If f has an absolute minimum value at c, then f '(c) = 0. (3). If f is continuous on (a, b), then f attains an absolute maximum value f(c) and an absolute minimum value f(d) at some numbers c and d in (a, b). (4). If f is differentiable and f(?1) = f(1), then there is a number c such that | c |< 1 and f '(c) = 0. (5). If f '(x) < 0 for 1 < x < 6, then f is decreasing on (1, 6). (6). If f ''(2) = 0, then (2, f(2)) is an inflection point of the curve y = f(x). (7). If f' (x) = g '(x) for all 0 < x < 1, then f(x) = g(x) for 0 < x < 1.

Explanation / Answer

http://www.math.uconn.edu/~judge/math1126s12/Ch4TrueFalseSolutions.pdf

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