Emily is in the process of building her own house and she is keen for her front door to be as large and impressive as possible. Emily managed to source a large piece of timber with a 'cross-sectional area' in the shape of a parabola, with one perfectly flat edge. When stood up on the flat edge, Emily determined (through some clever and mysterious methods) that the curved edge of the timber could be mapped using the function: h(w) = 3w (12-5w) 7 for 0 ≤ w ≤ 12 5 Where 'w' represents the 'width' (measured from the bottom left corner) and 'h' represents the height of the timber in metres. Emily drew the following image to help her visualise the problem. I h(w) Although Emily is determined for her house to be 'eye-catching', she is still somewhat conservative and wants the front door to be rectangular in shape and she is going to use the flat edge that is already present as one of the edges of the rectangle. Image 1: cross sectional shape of timber What is the largest possible rectangular door (in terms of area) Emily can cut from the piece of timber described above? (We are assuming that she is going to cut a single rectangular piece)