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**Unformatted text preview: **MATH 2413 weekly review week of 10/17 Topics: 1. Mean Value Theorem 2. increasing, decreasing and concavity 3. L’Hospital’s Rule 1. Show the hypothesis of Rolle’s theorem apply to the function on [0 , 2 π ]. Find all values guaranteed by the theorem. f ( x ) = sin(2 x ) + 2 cos( x ) 2. Show the hypothesis of the Mean Value Theorem apply to the function on [ 1 2 , 2]. Find all values guaranteed by the theorem. f ( x ) = x + 1 x 3. Prove the following inequality using the Mean Value Theorem. x 1 + x 2 < arctan( x ) < x 4. For the given function find all critical numbers, intervals where the function is increasing and decreasing and all relative extrema. f ( x ) = 3 x 2 / 3 ( x 2- 36) 5. For the given function find all critical numbers, intervals where the function is increasing and decreasing and all relative extrema. f ( x ) = 12 x 5 / 2- 45 x 2- 20 x 3 / 2 + 90 x 6. For the given function find all critical numbers, intervals where the function is increasing and decreasing and all relative extrema. f...

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