Refer to Table 1. (a) Using difference quotients, approximate /T and /S at the points (S, T) = (30, 2), (32, 6), and (35, 10).

Refer to Table 1.

(a) Using difference quotients, approximate ∂ρ/∂T and ∂ρ/∂S at the points (S, T) = (30, 2), (32, 6), and (35, 10).
(b) For fixed salinity S = 32, determine whether the quotients Δρ/ΔT are increasing or decreasing as T increases. What can you conclude about the sign of ∂²ρ/∂T² and the concavity of ρ as a function of T?

TABLE 1 Seawater Density p as a Function of Temperature T and Salinity S 31 32 23.51 24.27 T S 12 10 8 6 4 2 0 30 34 35 36 25.82 26.6 27.36 26.17 26.99 27.73 26.5 27.28 29.09 26.77 27.55 28.35 27.8 28.61 27.18 28.01 28.78 28.91 33 22.75 25.07 23.07 23.85 24.62 25.42 23.36 24.15 24.93 25.73 23.62 24.44 25.22 26 23.85 24.62 25.42 26.23 27 24 24.78 25.61 26.38 24.11 24.92 25.72 26.5 27.34 28.12