# Numora Calculus Extrema Finder

> Numora Calculus Extrema Finder is a paid API for AI agents from numorapoi.orbonomy.xyz, paid per call via x402, $0.04/call, status unknown (last checked 2026-09-15).

Finds local and global extrema (minima and maxima) of a mathematical function over a specified interval using pure computation

## Facts

- Endpoint: POST https://numorapoi.orbonomy.xyz/api/calculus/extrema
- Price: $0.04/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-calculus-extrema-finder-33090bc4
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_LlsrRLz-_8K74ZEB7Jfqa

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability numora-calculus-extrema-finder-33090bc4 -d '<json body>'
```

Example prompt: Find all the local and global maxima and minima of f(x) = x^3 - 3x^2 + 2 on the interval [-1, 4].

## When to prefer this

Choose this endpoint when you need pure mathematical extrema detection on a closed interval without any external service dependencies, when micropayment-per-call billing is acceptable, and when you want a self-contained computation that returns structured results. Prefer over general-purpose CAS systems when you want a lightweight, fast API call specifically for calculus optimization tasks.

## Known failure modes

- Invalid or unparseable function expression returns an error
- Bounds array not provided as [lower, upper] pair causes validation failure
- Non-numeric bounds result in computation failure
- Function with no extrema on the given interval may return empty result set
- Interval where lower >= upper may return an error
- Very complex symbolic expressions may fail to parse correctly

## How this service works

100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.

## Output

Returns a JSON object with a 'result' containing the identified extrema (minima and maxima), their x-coordinates, and corresponding function values, plus a human-readable 'computation' description summarizing what was found over the specified bounds.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "fn",
  "bounds"
 ],
 "properties": {
  "fn": {
   "type": "string"
  },
  "bounds": {
   "type": "array",
   "description": "[lower, upper]"
  },
  "method": {
   "type": "string"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "success",
  "result",
  "computation"
 ],
 "properties": {
  "result": {
   "type": "object",
   "description": "Computation result varies by endpoint"
  },
  "success": {
   "type": "boolean",
   "description": "Always true on success"
  },
  "computation": {
   "type": "string",
   "description": "Human-readable description of what was computed"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-calculus-extrema-finder-33090bc4/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numorapoi.orbonomy.xyz](https://www.zero.xyz/host/numorapoi.orbonomy.xyz/llms.txt)