# A two-variable quadratic approximation

> ML Prep screening item.

- Stable ID: `math-calc-04-second-order-taylor`
- Collection: screening
- Area: Mathematics
- Topic: Calculus
- Origin: original
- Difficulty: medium
- Expected time: 5 minutes
- Skills: taylor-approximation, hessian
- Item JSON: https://mlprep.iwase.dev/item/math-calc-04-second-order-taylor.json

## Problem

For $f(x,y)=\log x+xy+y^2$, form the second-order Taylor approximation at
$(1,0)$ in increments $(h,k)$, then use it to approximate $f(1.1,0.2)$.


## Answer policy

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## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `math-calc-04-second-order-taylor`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.