Let $f ( x ) = x ^ { 2 / 3 }.$

question 247

Essay

Let $f ( x ) = x ^ { 2 / 3 }.$ (a) Find a linear approximation of f at x = 8:
(b) Use this linear approximation to estimate the value of the function at 7, 9, 7.99, and 8.01.(c) Make a table comparing your estimates with the actual function values. Discuss what this tells you about the linear approximation.(d) Graph the original function and its linear approximation over the interval [7; 9]. What does the graph tell you about the size of the difference between the function values and the linear approximation values?

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Definitions:

Nominal Wages

Are the wages paid to workers measured in current monetary terms, without adjustment for inflation.

Price Level

The average of current prices across the entire spectrum of goods and services produced in the economy, often used to measure inflation.

Real Wages

Refers to wages that have been adjusted for inflation, indicating the actual buying power of the compensation.

Labor-Productivity

A measure of the amount of goods and services produced by one hour of labor.