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?

If you assume that decreasing means $x<y \Rightarrow f(x)> f(y)$ then $(B)$ "must" be false
If you assume that decreasing means $x\leq y \Rightarrow f(x)\geq f(y)$ then $(B)$  might be true
If you assume that $f$ has a global maximum in the point $(-3,5)$ then $(D)$ "must" be false
If you assume that $f$ has a local maximum in the point $(-3,5)$ then $(D)$ might  be true
Note that only (A) "must" be true.
EDIT: Goblin is right to say that the question leaves margin to doubt. Since there is ambiguity, it's up to you to decide which ways to go.
