6. Answer all questions

10. A water treatment plant is on the south bank of a straight river that is 2 miles wide. A sewer pipe is to be built from the plant to tanks located on the north bank of the river 6 miles west of the refinery. The cost of laying pipe is 40 thousand dollars per mile over land to a point P on the south bank, and 80 thousand dollars per mile under the river to the tanks. Where should point P be to minimize the cost? Answers without justification will not receive credit, and be sure to show that your answer minimizes the cost. 11. A box with an open top is to be constructed from a square piece of cardboard, 4 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. Answers without justification will not receive credit, and be sure to show that your answer maximizes the volume. 12. Pat wishes to fence in a rectangular area, using the wall of her garage as one side, so only three sides need to be fenced. If she has 80 ft of fencing available, what is the maximum area that can be fenced in?4. Find a cubic polynomial with a critical point at r = 3, an inflection point at (2,4), and a leading coefficient of 1. 5. Find a function of the form y = ar' + br' + c that has a y-intercept of 5 and absolute maxima at (1, 7) and (-1, 7). 6. If f has the following properties, sketch the graph of f below. It should be clear where all asymptotes, local extrema and inflection points occur. . f'(x) >0 on the interval (0,5) . f(x) 0 on the intervals (-3, -2) U (7,00) . f"(z)