Question

Let $g(x, y, z)=0.01 x+0.02 y-0.03 z-0.05 .$ Complete the following sentences. a. g _ by _ units for every 1 unit of increase in z. b. g _ by _ units for every 1 unit of increase in x. c. by 0.02 units for every _.

Name: Problem 10, Chapter 15: Finite Mathematics and Applied Calculus
Uploaded: 2021-10-15T15:38:38-08:00
Duration: 2 min 15 s
Channel: Harshita Goel
Description: Let g(x, y, z)=0.01 x+0.02 y-0.03 z-0.05 . Complete the following sentences. a. g by units for every 1 unit of increase in z. b. g by units for every 1 unit of increase in x. c. by 0.02 units for every .

   Let $g(x, y, z)=0.01 x+0.02 y-0.03 z-0.05 .$ Complete the following sentences.
a. g ___ by ___ units for every 1 unit of increase in z.
b. g ___ by ___ units for every 1 unit of increase in x.
c. ______ by 0.02 units for every _______.

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 5th Edition

Chapter 15, Problem 10

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Solved by Expert Harshita Goel

10/15/2021

Step 1

01 x+0.02 y-0.03 z-0.05$. We need to determine how the function $g$ changes with respect to $x$, $y$, and $z$. Show more…

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Let $g(x, y, z)=0.01 x+0.02 y-0.03 z-0.05 .$ Complete the following sentences. a. g ___ by ___ units for every 1 unit of increase in z. b. g ___ by ___ units for every 1 unit of increase in x. c. ______ by 0.02 units for every _______.

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Key Concepts

Partial Derivative

In a multivariable function, a partial derivative measures the rate at which the function changes as one of the variables changes, while all other variables are held constant. This concept allows one to understand the individual effect of each variable on the overall function.

Coefficient Interpretation in Linear Functions

In the context of linear functions, each coefficient represents the constant rate of change of the function with respect to its corresponding variable. A positive coefficient indicates that the function increases with an increase in that variable, while a negative coefficient indicates that the function decreases.

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