Let $f ( x ) = \frac { x } { x ^ { 2 } + 25 }$

question 104

Essay

Let $f ( x ) = \frac { x } { x ^ { 2 } + 25 }$ .(a) Use your graphing calculator to graph f using the default viewing rectangle
.(b) Find the critical points of f and use them to determine an appropriate viewing rectangle (or rectangles) for f. The graph f again using the viewing rectangle.(c) Compare the graphs in parts (a) and (b)

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Definitions:

Break-Even Point

The level of production or sales at which total revenues equal total costs, resulting in zero profit.

Partial Moves

Actions or strategies that are implemented to a limited extent, often as a trial or preliminary step before full execution.

Margin of Safety

The difference between actual or projected sales and the break-even sales, indicating the risk cushion for not incurring losses.

Contribution Margin

The amount by which a product's sales price exceeds its variable costs, indicating how much it contributes to covering fixed costs and generating profit.