Concavity and Mean Value Theorem
Let $$t$$ be a twice-differentiable function on the interval $$[-3, 3]$$ with $$t(-3) = 12$$, $$t(0) = 9$$, and $$t(3) = 18$$. If $$t''(x) < 0$$ on the interval $$(-3, 0)$$ and $$t''(x) > 0$$ on the interval $$(0, 3)$$, which of the following must be true?
A
$$t'(0) = 0$$
B
$$t'(0) > 0$$
C
$$t'(0) < 0$$
D
The sign of $$t'(0)$$ cannot be determined from the given information
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