Let f(x, y, z) be the amount of heat lost each day by a rectangular building x feet wide, y feet long, and z feet high. Suppose that $\frac { \partial f } { \partial z }$ (50, 80, 15) = 45. Which one of the following conclusions can be drawn?
A) A building with dimensions 51 × 81 × 16 will lose about 45 more units of heat each day than a building with dimensions 50 × 80 × 15 .
B) A building with dimensions 50 × 80 × 15 loses about 45 units of heat each day.
C) A building with dimensions 50 × 80 × 16 will lose about 45 more units of heat each day than a building with dimensions 50 × 80 × 15 .
D) A building with dimensions 50 × 80 × 15 loses about 45 units of heat from the top of the building each day
E) The marginal heat loss per day is 45 units of heat per square foot of surface area of the roof.

Question

Quizplus · Accepted Answer

The partial derivative $\frac { \partial f } { \partial z }$ represents the rate of change of the heat lost with respect to the height of the building. A value of 45 at the point (50, 80, 15) means that increasing the height from 15 to 16 (a unit increase in z) while keeping the other dimensions constant will increase the heat loss by approximately 45 units.

Let F(x, Y, Z) Be the Amount of Heat Lost ∂f∂z\frac { \partial f } { \partial z }∂z∂f​

Let F(x, Y, Z) Be the Amount of Heat Lost $\frac { \partial f } { \partial z }$