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Suppose f'(x) is continuous over an interval ? ? x ? b, and a <...

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Calculus

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Suppose f'(x) is continuous over an interval ? ? x ? b, and a < c < d < b.If f'(c) = 5, then (check all that apply)f(x) is decreasing through x = cf(c) = 5f(c) existsf does not have a minimum at x = cf does not have a maximum at x = cf(x) is increasing through x = cIf f'(d) = -5, then (check all that apply)f(d) existsf does not have a maximum at x = df does not have a minimum at x = df(d) = -5f(x) is increasing through x = df(x) is decreasing through x = dBased on this, we know that for some x between x = c and x = d:f has a maximumf has a minimumf does not existf'(x) = 0

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