Use Differentials to Approximate the Change in the Function $f ( x ) = x ^ { 2 } + x - 2$

question 105

Essay

Use differentials to approximate the change in the function $f ( x ) = x ^ { 2 } + x - 2$ when x varies from 1 to 1.01.

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Definitions:

Optimal Number

The most favorable, efficient, or effective quantity or value given a certain context or criteria.

Monthly Profit

The total revenue of a business minus its expenses, costs, and taxes calculated on a monthly basis.

Total Optimal Profit

The maximum possible profit that can be achieved in a given scenario, taking into account all constraints and limitations.

Solver

A software tool used in optimization that finds the optimal solution to a problem by varying the values of variables within constraint boundaries.