Mathematics Homework Help

Hello!

Would you please be able to help me with this question for a finance course. This question is more heavy on statistics and calculus so I decided to put it in the “mathematics” category. The question is about the Black-Scholes PDE and using it to prove some things. It’s hard to explain out of context in this description, so I have attached the question. The question refers to certain slides off of a lecture, so I have included that in the same folder as the question. In particular slides 21-24.

If you could help me with this question, I would be very grateful!

Thank you!