A metal plate is situated in the xy-plane and occupies the rectangle 0 ≤ x ≤ 10, 0 ≤ y ≤ 8, where x and y are measured in meters. The temperature at the point (x, y) in the plate is T(x, y), where T is measured in degrees Celsius. Temperatures at equally spaced points were measured and recorded in the table.

(a) Estimate the values of the partial derivatives T_x(6, 4) and T_y(6, 4). What are the units?

(b) Estimate the value of D_u T(6, 4), where u = (i + j)/√2 . Interpret your result.

(c) Estimate the value of Txys6, 4d.

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y 6 8 30 38 45 51 55 52 56 60 62 61 4 78 74 72 68 66 98 71 6 87 80 75 96 90 86 80 75 10 92 92 91 87 78 4, 2. 2.