Math & Numbers
Newton-Raphson Root Finder
Newton-Raphson iteration for f(x) = 0 with analytic or numeric derivative, full iteration table, and explicit convergence/divergence reporting.
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Quick start
Call this tool from your code in three languages.
cURL
curl -X POST 'https://api.elysiatools.com/en/api/tools/newton-raphson-root-finder' \
-H 'Content-Type: application/json' \
-d '{"fxExpr":"x^2 - 2","dfxExpr":"","x0":1,"tolerance":1e-10,"maxIter":50,"decimalPlaces":10}'API reference
Send a POST request with your inputs as JSON. File parameters require a separate upload first.
Endpoint
HTTP
POST https://api.elysiatools.com/en/api/tools/newton-raphson-root-finderParameters
| Name | Type | Required | Description |
|---|---|---|---|
| fxExpr | text | Yes | The function whose root is sought, in the variable x. Supports + - * / ^, parentheses, and functions like exp, sin, cos, sqrt, ln. |
| dfxExpr | text | No | Optional analytic derivative; when blank a central difference (h ≈ 1e-7) is used. |
| x0 | number | No | Starting point of the iteration. |
| tolerance | number | No | Convergence threshold on |f(x)| and on the step size. |
| maxIter | number |
MCP integration
Add this tool to your Model Context Protocol server so AI agents can list and call it.
Server configuration
Add this block to your MCP client configuration:
mcp.json
{
"mcpServers": {
"elysiatools-newton-raphson-root-finder": {
"name": "newton-raphson-root-finder",
"description": "Newton-Raphson iteration for f(x) = 0 with analytic or numeric derivative, full iteration table, and explicit convergence/divergence reporting.",
"baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=newton-raphson-root-finder",
"command": "",
"args": [],
"env": {},
"isActive": true,
"type": "sse"
}
}
}List available tools
After connecting to the SSE endpoint, list the exposed tools:
tools/list
{
"jsonrpc": "2.0",
"id": 1,
"method": "tools/list"
}Call this tool
Invoke the tool by its id, passing arguments built from its parameters:
tools/call
{
"jsonrpc": "2.0",
"id": 2,
"method": "tools/call",
"params": {
"name": "newton-raphson-root-finder",
"arguments": {
"fxExpr": "x^2 - 2",
"dfxExpr": "",
"x0": 1,
"tolerance": 1e-10,
"maxIter": 50,
"decimalPlaces": 10
}
}
}Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).
Questions or issues? Contact [email protected]