Help with confirming if my answer is correct (derivatives)?

[kaonashi]

Hello! I posted this question recently and was able to finally solve it with the help of the comments (thank you so much!). I am posting it again with my solution. Please let me know if I did the correct thing and if my answer is right.

P.S.: If the scanned photo of my solution is hard to read, my answer is y=x+15/4.

Thanks a bunch!

 

[HallsofIvy]

You do not say, even in the working you show, tell us what the problem to be solved was! Is this the same problem as "Please help me with a problem on derivatives and differentiability"?

 

[kaonashi]

Hello! I attached a screenshot of the question to the problem.

 

[Debsta]

Hello! I attached a screenshot of the question to the problem.

Well done. Your solution is correct.