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11. pes)Determine the x-coordinates of the points of absolute maximum and absolute minimum of the function S(x) = x - 2 sin x over the interval (0) points) of absolute minimum at x point(s) of absolute maximam atx 12.9 pts) Consider the function f(x) = x+3x7-9x+7. Determine the intervals on which S(x) is increase ing/decreasing and tind the points of local (relative) maximum/minimum, if any. Sax) is increasing on f(x) is decreasing on: points) of local (relative) minimum at ** points) of local (relative) maximum at x = 13.9 pts) Find all intervals where the function(x) = +8In(x) is concave up. (Note/(x) is defined only for x > 0) concave up on
6- 14. (8 pts) A rectangle is bounded by the axis, the axis and the graph of the line ya What length and width should the rectangle have so that its area is maximum? Obtain and justify your answer using the methods of Calculus. 6- ia 2 2 x.y) 1 2 3 4 5 6 y 15. (8 pts) You are inflating a spherical balloon at the rate of 7 cm/sec. How fast is its radius increasing when the radius is 4 cm? (The volume of a sphere is V = rate