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:

Single Plantwide Factory Overhead Rate

A method of allocating total factory overhead costs to units produced, using a single rate for the entire manufacturing plant.

Labor-Intensive Department

A department within a company that relies more on human labor than on machinery or automation to produce goods or provide services.

Capital-Intensive Department

A division within a company that requires a large investment in capital assets relative to its labor cost.

Single Plantwide Factory Overhead Rate

A method of allocating total factory overhead to products based on a single rate, often using total direct labor hours or machine hours.