Properties of a Continuous Function

Question

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?

Accepted Answer

$$w$$ has a local minimum between $$x = 4$$ and $$x = 6$$

Answer

$$w$$ has a local maximum between $$x = 0$$ and $$x = 2$$

Answer

$$w$$ has both a local maximum and a local minimum between $$x = 6$$ and $$x = 8$$

Answer

$$w$$ is strictly increasing on the interval $$[4, 6]$$

Rank	User	Correct Count	Attempt Count	Total Time	Score
#1	triptigoyal02	2	2	0m 00s	200
#2	haneesh19.12	1	1	0m 00s	100
#3	toilaminh28122008	1	1	1m 27s	13
#4	iveara0	0	1	0m 00s	-10
#5	daniel.rufener	0	1	5m 20s	-330

Properties of a Continuous Function

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