1. ($4.1, 5pts each) Find the critical numbers of each of the following functions. Then determine the intervals where each function is increasing and decreasing. a. f(x) = 2x3 - 15x2 + 22x + 15 b. g(x) = r In(x) - r c. h(r)=re2. ($4.6, 10pts) Find the dimensions of a rectangle with an area of 320m that has a minimum perimeter. 3. ($4.6, 10pts) Find the dimensions of a rectangle with a perimeter of 85m that has a maximum area.4. ($4.6, 15pts) A fence is to be built to enclose a rectangular area of 500 square feet. The north side of the area is being built adjacent to a river. Hence, the northern side of the fencing must be built with special waterproof material, which costs $25 per foot. The other three sides of the fence are built with standard material, which costs $10 per foot. Find the dimensions of the rectangular area that will allow for the most economical fencing