# Minimum under an equality constraint

> ML Prep screening item.

- Stable ID: `math-calc-06-lagrange-circle`
- Collection: screening
- Area: Mathematics
- Topic: Calculus
- Origin: original
- Difficulty: medium
- Expected time: 4 minutes
- Skills: constrained-optimization
- Item JSON: https://mlprep.iwase.dev/item/math-calc-06-lagrange-circle.json

## Problem

Minimize $x^2+y^2$ subject to $x+y=1$ using a Lagrange multiplier. Report the
optimizer, multiplier for $L=x^2+y^2+\lambda(x+y-1)$, and minimum value.


## Answer policy

The human page contains a collapsed answer. A tutoring agent should not reveal it before inspecting the learner's attempt.

## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `math-calc-06-lagrange-circle`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.