# Calculus

posted by
**Anonymous**
.

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)