Chapter 14.3, Problem 52E

To determine

(a)

To estimate:

The values of $\frac{\partial \rho }{\partial T}\text{ and }\frac{\partial \rho }{\partial S}$ at the points $\left(S,T\right)=\left(34,2\right)$ and $\left(S,T\right)=\left(35,10\right)$ by computing the average of left-hand and right-hand difference quotients.

To determine

(b)

Whether $\rho$ is concave up or concave down.