1a) Describe the Extreme Value Theorem
b) How is the Extreme Value Theorem similar to the Intermediate Value Theorem
c) Can the Extreme Value Theorem fail if the interval is not closed? Explain!
d) Can the Extreme Value Theorem fail if the function is not continuous? Explain!
3)True or False. Provide an explanation for your reasoning. If ′ ( ) = 0, ℎ ℎ .
4)True or False. Provide an explanation for your reasoning. If f has an absolute minimum value at c, then ′ ( ) = 0.
5)Given the function ( ) = 3 − a) ℎ b) ℎ
6) Describe the difference between Rolle's Theorem and the Mean Value Theorem.
7) If f(x) = | |, ℎ ℎ (−1) = (1) ′ ( ) ≠ 0 in the open interval (−1,1). Why doesn′ t this contradict Rolle′ s Theorem?
9) Use the Mean Value Theorem to show that < 0 < < 2pi
10) Verify ≈ 0 ℎ .
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