Ρ(S, T) is seawater density (kilograms per cubic meter) as a...

$ \rho(S, T)$ is seawater density (kilograms per cubic meter) as a function of salinity $S$ (parts per thousand) and temperature $T$ (degrees Celsius). Refer to the contour map in Figure $25 .$
Calculate the average rate of change of $\rho$ with respect to $S$ from $B$ to $C$.

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Key Concepts

Average Rate of Change

The average rate of change of a function between two points is defined as the difference in the function's values at those points divided by the difference in the corresponding input values. It provides a measure of how much the function changes, on average, per unit change in the input.

Difference Quotient

The difference quotient is the expression used to calculate the average rate of change of a function over an interval. It is computed as the ratio of the change in the function's output to the change in the input, serving as a finite approximation to the derivative.

Multivariable Functions

Multivariable functions involve two or more independent variables and their interactions in determining the output. Understanding these functions often requires analyzing how the function changes with respect to one variable while keeping the others fixed, which is foundational in studying partial derivatives and directional rates of change.

Contour Map

A contour map graphically represents a function of two variables by drawing curves that connect points of equal function value. This visualization is useful for understanding the topography of the function, identifying regions of rapid change, and estimating gradients, which can help in calculating average rates of change along specific directions.

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