Suppose that f(x, y) = x - xy+ y - 4x + 4y with x + y 16. 1. Absolute minimum of f(x, y) is 2. Absolute maximum is Apply a second derivative to identify a critical points as a local maximum, local minimum or saddle point for a function. Suppose that f(x, y) = 2x + 2y 2xy then the minimum is Submit Question Apply a second derivative to identify a critical points as a local maximum, local minimum or saddle point for a function. The following three lines do not have a common intersection: x + y = 2, x=y=3 and x + 2y = 4. However, we can find an "approximate solution" to this system of equations by finding a point (x, y) that is in some sense as close as possible to all three lines, simultaneously. d Find the coordinates of the point that minimizes the sum of the squares of the distances to each line, d +d +d. Hint: The distance of a point (x, y) to a line ax + by - c = 0 is given by Please show exact answers as whole numbers, decimals or fractions. lax + by - c a +6 Apply a second derivative to identify a critical points as a local maximum, local minimum or saddle point for a function. An open-top rectangular box is being constructed to hold a volume of 250 in. The base of the box is made from a material costing 7 cents/in. The front of the box must be decorated, and will cost 12 cents/in. The remainder of the sides will cost 4 cents/in. Find the dimensions that will minimize the cost of constructing this box. Please show your answers to at least 4 decimal places. Front width: Depth: Height: Question Help: Video in. in. in. Apply a second derivative to identify a critical points as a local maximum, local minimum or saddle point for a function. An engineer is designing a pipeline which is supposed to connect two points P and S. The engineer decides to do it in three sections. The first section runs from point P to point Q, and costs $52 per mile to lay, the second section runs from point Q to point R and costs $40 per mile, the third runs from point R to point S and costs $38 per mile. Looking at the diagram below, you see that if you know the lengths marked x and y, then you know the positions of Q and R. Find the values of x and y which minimize the cost of the pipeline. Please show your answers to 4 decimal places. P 2 Miles X = y = 1 Mile A 10 miles miles miles (0) S