Posted by Anonymous on Friday, December 21, 2012 at 1:15pm.
Suppose that f(x), f'(x), and f''(x) are continuous for all real numbers x, and the f has the following properties.
I. f is negative on (inf, 6) and positive on (6,inf).
II. f is increasing on (inf, 8) and positive on 8, inf).
III. f is concave down on (inf, 10) and concave up on (10, inf).
Of the following, which has the smallest numerical value?
(a) f'(0)
(b) f'(6)
(c) f''(4)
(d) f''(10)
(e) f''(12)

Calculus  Steve, Friday, December 21, 2012 at 2:41pm
i) > f'(0) > 0
i) > f'(6) > 0
iii) > f"(4) < 0
iii) > f"(10) = 0
iii) > f"(12) > 0
so f"(4) is the only negative value

Calculus  Steve, Friday, December 21, 2012 at 2:41pm
sorry, (ii) relates to f', not (i)
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