Let $$p$$ be a twice-differentiable function on the interval $$[1, 7]$$ with $$p(1) = 4$$, $$p(4) = 10$$, and $$p(7) = 22$$. The average rate of change of $$p$$ from $$x = 1$$ to $$x = 4$$ is $$2$$, and the average rate of change from $$x = 4$$ to $$x = 7$$ is $$4$$. If $$p''(x) > 0$$ for all $$x$$ in $$(1, 7)$$, which of the following statements about $$p'(4)$$ must be true?