Lab 4B: AI Numerical Answer Review

Goal

Practice reviewing AI-generated numerical work that gives an answer without enough evidence.

Scenario

A student asks an LLM:

Solve this equation numerically: x^3 - 6x^2 + 11x - 6 = 0.

The generated script resembles week04_ai_numeric_review.m.

Part A: Run The Script

  1. Open the script.
  2. Run it without editing.
  3. Record the printed answer.
  4. Record the initial guess used by the code.
  5. Decide whether the script proves that there is only one solution.

Part B: Add Evidence

Modify the script to:

  1. Plot the function on [0, 4].
  2. Add a horizontal line at zero.
  3. Use brackets to find each root.
  4. Compute the residual at each root.

Part C: Name The Missing Checks

Complete the table.

Missing check Why it matters
Plot before solving
Brackets or multiple guesses
Residual f(root)
Statement of method limits

Part D: Repair The Claim

Rewrite the generated conclusion so that it is mathematically honest. It should mention:

  • the equation;
  • all roots found on the checked interval;
  • the residuals;
  • the interval you inspected.

Deliverable

Submit:

  • the original generated claim in one sentence;
  • the repaired claim;
  • one plot;
  • the residual table;
  • a short explanation of why the original output was incomplete.

Exit Question

Complete this sentence:

A generated numerical answer is not trustworthy until …