# Convexity and stationary points

> ML preparation item.

- Stable ID: `original-ml-optimization`
- Area: Machine Learning
- Topic: Optimization
- Origin: original
- Expected time: 8 minutes
- Skills: objective-functions, stationary-points, convexity, optimization-diagnostics
- Item JSON: https://mlprep.iwase.dev/data/items/original-ml-optimization.json

## Problem

Compare $f(w)=w^2+2w+5$ and $g(w)=w^4-w^2$. Identify stationary points and state which objective is convex on the real line.


## Answer policy

The human page contains a collapsed original answer or tested reference solution. 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 `original-ml-optimization`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.