If the function is f x,y =1+2x + 3xy + 4y 2 , derive the x–y relation that represents the line of steepest descent from the (x, y) pair (2, 2). Figure 7.10 shows a contour of a 2-DV application, and...

If the function is f x,y =1+2x + 3xy + 4y², derive the x–y relation that represents the line of steepest descent from the (x, y) pair (2, 2).

Figure 7.10 shows a contour of a 2-DV application, and the x-marks indicate the local (upper left) and global (lower right) optima. At the DV1 = 4 and DV2 = 5 point, sketch the tangent to the contour and the negative gradient. Repeat for DV1 = 1 and DV2 = 4 point, and sketch the tangent to the contour and the negative gradient.