Improve cake eating lecture with new exercise and fixes

[jstac]

Summary

This PR improves the cake eating lecture with several enhancements:

• New exercise: Added exercise cep_ex2 asking readers to verify that the optimal policy σ* satisfies the Euler equation, including a complete step-by-step solution showing the algebraic verification
• Grammatical fixes:
  • Fixed "the same it was" → "the same as it was"
  • Fixed "Here's some plots" → "Here are some plots" (subject-verb agreement)
  • Fixed "This is necessary condition" → "This is a necessary condition" (missing article)
• Clarified assumptions: Added a note in Derivation II clarifying that we assume the value function is differentiable, with reference to EDTC theorem 10.1.13 for the proof
• Improved consistency: Made the text reference to the exercises consistent with what is actually asked (line 363 now correctly points to the new cep_ex2 exercise)

Test plan

• Verified all grammatical corrections read naturally
• Confirmed new exercise solution is mathematically correct
• Checked EDTC reference follows the format used elsewhere in the codebase
• Ensured MyST syntax is correct for the new exercise and solution blocks

🤖 Generated with Claude Code

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-718--sunny-cactus-210e3e.netlify.app (2c89670)

📚 Changed Lecture Pages: cake_eating