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Math 151 WIR 9, Spring Semester 2015 © Dr. Rosanna Pearlstein Sections 5.1, 5.2, 5.3, 5.5. 1. The graph of the second derivative f " of function f is shown below a) For what value(s) of x does f ' have a local maximum or minimum? b) For what value(s) of x is the graph of f concave up? c) For what value(s) of x is the graph of f concave down? d) Where are the points of inflection of the graph of f located? 2. Find the following limits: a. limπ₯→+∞ lnx ππ₯ b. limπ₯→+∞ √π₯ 2 − 6π₯ − π₯ π₯+πππ π₯ c. limπ₯→+∞ π₯+π πππ₯ 3. Find the absolute maximum and absolute minimum values of f on the given interval. π(π₯) = π πππ₯ + πππ π₯ in [0, 2π]. Math 151 WIR 9, Spring Semester 2015 © Dr. Rosanna Pearlstein 4. Do all the necessary math to sketch the graph of π(π₯) = π₯π −π₯ . 5. Find the absolute maximum value and the absolute minimum value attained by 1 π(π₯) = π₯(1−π₯) in the interval [2,3]. 6. Do all the necessary math to sketch the graph of π(π₯) = π₯ 2 + 16 π₯ . 7. Find the absolute maximum value and the absolute minimum value attained by π(π₯) = π₯1/2 + π₯ 3/2 in the interval [0,4]. 8. What angle between two edges of length 3 will result in an isosceles triangle with the largest area? (See diagram.) 9. A cylindrical can is made to hold 1 liter of oil. Find the dimensions of the can that will minimize the cost of the metal to manufacture the can. 10. Find all points on the curve π₯ 2 − π¦ 2 = 1 that are closest to the point (0, 2).