MAT 137 LEC 0601 Instructor: Alessandro Malus TA: Julia Kim - - PowerPoint PPT Presentation

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Apr 08, 2024 25 likes •85 views

MAT 137 LEC 0601 Instructor: Alessandro Malus TA: Julia Kim October 15th, 2020 Warm-up question : Is this correct? Consider the function f ( x ) = 1 x . We have that f ( 1) = 1 < 0 and f (1) = 1 > 0. By IVT, there exists c

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MAT 137 — LEC 0601

Instructor: Alessandro Malusà TA: Julia Kim October 15th, 2020 Warm-up question: Is this correct? Consider the function f (x) = 1 x . We have that f (−1) = −1 < 0 and f (1) = 1 > 0. By IVT, there exists c ∈ (−1, 1) such that f (c) = 0.

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Existence of solutions

Prove that the equation x4 − 2x = 100 has at least two solutions.

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Can this be proven? (Use IVT)

1 Prove that the hour hand and the minute hand of a clock

form an angle of exactly 23 degrees at least once a day.

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Can this be proven? (Use IVT)

1 Prove that the hour hand and the minute hand of a clock

form an angle of exactly 23 degrees at least once a day.

2 During a Raptors basketball game, at half time the Raptors

have 52 points. Prove that at some point they had exactly 26 points.

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Extrema

In each of the following cases, does the function f have a maximum and a minimum on the interval I?

1 f (x) = x2,

I = (−1, 1).

2 f (x) = (ex + 2) sin x

x − cos x + 3, I = [2, 6]

3 f (x) = (ex + 2) sin x

x − cos x + 3, I = (0, 5]

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Before next class...

Watch videos 3.1, 3.2, and 3.3.
Download the next class’s slides (no need to look at them!)