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Math-150-Exam-3-Fall-2016.docx

Math-150-Exam-3-Fall-2016.docx - 1 Let f x x 2 8 ln x x 0...

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1. Let x x x f ln 8 2 ) ( , 0 x . a . (5 pts) Find the intervals on which f is increasing or decreasing. b . (5 pts) Find the (x,y) coordinates of any local maximum or minimum point(s) of f . Justify your answer(s). 2. Suppose f is a function whose second derivative given by 3 2 2 1 ) ( x x x x f , a. (3 pts) Find the interval(s) on which f is concave up or concave down. b. (2 pts) Find the s coordinate x of the inflection points. 3. Evaluate each limit. State the indeterminate form at each step when using L’Hospital’s Rule. Simplify your answers! a. (5 pts) 2 0 1 6 lim 6 x x x x e b. (5 pts) x x x / sin lim Hint: f g fg / 1
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4. (10 pts) A function f is continuous and has the following properties. Sketch a graph of f . Properties: 0 ) 2 ( f , 0 ) 2 ( f , ) 0 ( f is undefined, 1 ) 2 ( f , and the signs of ) ( x f and ) ( x f given below. 4 2 3 2 1 1 2 3 2 ) ( x f 2 0 2 ) ( x f 0 5. The graph of the derivative of a continuous function f is shown below. The domain of
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