Suppose f'(x) is continuous over an interval α ≤ x ≤ b, and a

Question

Suppose f'(x) is continuous over an interval α ≤ x ≤ b, and a < c < d < b.
If f'(c) = 5, then (check all that apply)
f(x) is decreasing through x = c
f(c) = 5
f(c) exists
f does not have a minimum at x = c
f does not have a maximum at x = c
f(x) is increasing through x = c
If f'(d) = -5, then (check all that apply)
f(d) exists
f does not have a maximum at x = d
f does not have a minimum at x = d
f(d) = -5
f(x) is increasing through x = d
f(x) is decreasing through x = d
Based on this, we know that for some x between x = c and x = d:
f has a maximum
f has a minimum
f does not exist
f'(x) = 0

Kunduz · Accepted Answer

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