# Classify all stationary points

> ML Prep screening item.

- Stable ID: `math-calc-05-critical-classification`
- Collection: screening
- Area: Mathematics
- Topic: Calculus
- Origin: original
- Difficulty: hard
- Expected time: 6 minutes
- Skills: calculus-stationary-points, unconstrained-optimization, calculus-convexity
- Item JSON: https://mlprep.iwase.dev/item/math-calc-05-critical-classification.json

## Problem

Find and classify every critical point of $f(x,y)=x^4-2x^2+y^2$. Is $f$ convex
on all of $\mathbb R^2$?


## 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-05-critical-classification`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.