High-School Calculus & Matrix Help

I have a single high-school level math problem that mixes introductory Calculus ideas with basic matrix operations. I need a complete, clearly written solution that walks through every step, explains the reasoning in plain language, and finishes with the final numeric or algebraic answer.

Please keep the explanation accessible to a student at secondary-school level—no skipped steps, no unexplained shortcuts—and show each matrix calculation in detail so I can follow and learn from the process.

Deliverables
• A neatly formatted solution (typed in LaTeX, Word, or a clean PDF)
• Any supporting work or scratch calculations, if they help illuminate the method

Once I can read through your solution without stumbling on any gaps, I’ll consider the job done.