Which statement "must be false"? Given a function $f$ continuous on $[-4, 1]$ with its maximum at $(-3, 5)$ and its minimum at $(1/2, -6)$, is it not correct to say that both statements (B) and (D) must be false?
(A) The graph of $f$ crosses both axes.
(B) $f$ is always decreasing on $[-4, 1]$.
(C) $f(-2)=0$,
(D) $f(-1)=6$,
(E) $f(0)=2$.
If the maximum (on this interval at least) is $(-3, 5)$, then $(-1, 6)$ cannot be a point on the graph (D). That the function is "always decreasing" (B) on the interval seems to contradict both the stated maximum and stated minimum. The other options all seem either certainly true or possible. Am I missing something?

There is no reason the function needs to be monotonic between (-3,5) and (1/2,-6). Many authors,e.g. Bourbaki,use decreasing to mean non-increasing, rather than strictly decreasing. It cannot be strictly decreasing if its max and min occur strictly between the end points of its domain. The values in (C) and (E) are consistent but cannot be inferred, which  means they are possible.
