1. For f(x)=x^4 - 4x^3 + 4x^2 find all local and absolute maximum, and minimum values on the interval [-1, 3], For each point found, state if local or absolute and max or min. 2. A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola y = 36 - x^2 . What are the dimensions of the rectangle with the maximum area? What is the maximum area? 3. A square with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 5ft x 8 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way. Maximum Volume = _______ 4. Determine if L'Hopital's Rule can be applied to the following limit. If so, use L'Hopital's Rule to evaluate the limit. a) lim x> 0 (e^x - 1) / (x^2+3x) b) lim x> 2pi (xsinx + x^2 - 4pi^2) / (x - 2pi)