Use Differentials to Approximate the Arc Length of the Graph $\mathbf { P }$

question 35

Short Answer

Use differentials to approximate the arc length of the graph of the equation from $\mathbf { P }$ to $\mathbf { Q }$ . Round answer to four decimal places.
$$y = x ^ { 3 } + 3 ; \mathrm { P } ( 1,4 ) , \quad \mathrm { Q } ( 1.2,4.728 )$$

---

Definitions:

Operating Leverage

A measure of how revenue growth translates into growth in operating income, indicating the proportion of fixed costs in a company's cost structure.

Operating Income

The profit realized from a business's core operations, calculated before interest and taxes are deducted.

Break-even Point

The level of production or sales at which total costs equal total revenue, meaning no net loss or gain is incurred; a crucial financial analysis metric.

Break-even Point

The break-even point is the level of production or sales at which total revenues equal total expenses, resulting in no net profit or loss.