Report Requirements Checklist

2-5 page report describing a calculus application.
Concrete example with computation and visuals.
Works cited section (not counted in page limit).
Individual contribution + reflection paragraphs.
Short presentation-ready summary.

Quick Summary

Software teams rely on calculus to translate observed data into decisions about scaling, deployment safety, and cost efficiency. By modeling latency with a differentiable curve, we can compute the traffic level that minimizes response time and plan ahead.

Interactive Model

Adjust the coefficients to match your own load-test data. The derivative highlights where latency grows fastest.

a (curvature)0.020

b (linear)-1.2

c (baseline)35

x (drag point)12.0

zoom1.0x

show tangentmark extremum

L(x) = 0.020x^2 - 1.2x + 35

L'(x) = 0.040x - 1.2

Drag point: $x_0 = 12.0$ , slope $L'(x_0) = -0.72$ . Optimal load: $x^* = 30.0$ with latency about $17.0,ms$ .

Numeric Table

x	L(x)	L'(x)
-50.0	145.00	-3.20
-25.0	77.50	-2.20
0.0	35.00	-1.20
25.0	17.50	-0.20
50.0	25.00	0.80

Interactive Graph

The curve is rendered directly inside the site. This snapshot is captured and embedded into the exported PDF.

Team Spotlights

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Sawyer

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Individual Contribution

I designed the latency model, implemented the interactive graph, and summarized how calculus supports capacity planning in microservice systems.

Reflection

This project helped me connect derivatives to real engineering choices. I now see how performance tuning relies on understanding rates of change, not just absolute numbers.

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Sawyer