1. Consider the function f x x x ( ) 2cos( ) = + on [0, 2𝛑]. A...

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1. Consider the function f x x x ( ) 2cos( ) = + on [0, 2𝛑]. Answers must be exact. (7 points) c. What are the local maximum or minimum for the function? 2. Find the inflection points for the following function, and determine the intervals of concavity. 𝑓(𝑥) = 8𝑥 + 2 − 𝑠𝑖𝑛𝑥, 0 < 𝑥 < 3𝜋 3. Find the absolute maximum and minimum values of 2 ) +1 x f x( x x = − on the interval [0, 3]. 4. Verify that f x( ) 2 = x +1 tsatisfies he hypotheses of the Mean Value Theorem on [0, 8]. Find the number c that satisfies the conclusion of the theorem. 9. Use Calculus and the following function to answer the questions below. 3 2 + 4 ) x f x( x = a. What is the domain of f x( ) ? Write your answer in interval notation. d. On what interval(s) is 𝑓(𝑥) increasing? e. On what interval(s) is 𝑓(𝑥) decreasing? f. Identify any local minima or maxima. Write your answer as coordinate points. 13. The graph of the derivative is shown, f’(x). a. State where f(x) is increasing and decreasing. b. State the critical points. c.State where the graph is concave up and concave down.

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