You posted way too many questions. The rule is one question at a time.
I'll answer question 14 to get you started.
We are told that
The values -1 and 1 don't really matter. All we care about is the sign change from negative to positive or vice versa. This sign change tells us that f(x) must be zero at least once in the interval [4, 6]. Refer to the intermediate value theorem for more information. Therefore, we have at least one root in the interval [4, 6].
Visually you can think of it like being in United States (below the x axis; negative territory) and then moving to Canada (above the x axis; positive territory). Since f(x) is a continuous function, the curve must cross the border at least once. The border represents the x axis. The term "root" is another way of saying "x intercept".
The previous paragraphs all help point to the fact that statement I is valid. Unfortunately, we don't have enough information to determine if statement II is valid or not. The function f(x) may have an absolute max on this interval, or it may not. We would need info about its derivative.
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Answer to problem 14 is "I only" which is choice B.