APFIVE Properties of a Continuous Function
A function $$w$$ is continuous on the closed interval $$[0, 8]$$ and satisfies $$w(0) = -3$$, $$w(2) = 7$$, $$w(4) = 1$$, $$w(6) = 11$$, and $$w(8) = -5$$. If the equation $$w(x) = 5$$ has exactly three solutions for $$x$$ in $$[0, 8]$$, which of the following must be true?
A
$$w$$ is strictly increasing on the interval $$[4, 6]$$
B
$$w$$ has both a local maximum and a local minimum between $$x = 6$$ and $$x = 8$$
C
$$w$$ has a local minimum between $$x = 4$$ and $$x = 6$$
D
$$w$$ has a local maximum between $$x = 0$$ and $$x = 2$$
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