Real-World Application: Apply the concept of differentiation to the following scenarios. Provide detailed calculations and explanations.
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- Use derivatives to optimize the profit function of a company, maximizing profit.
- Analyze the velocity and acceleration of a car given its position function s(t)=t3−4t2+2ts(t) = t^3 – 4t^2 + 2ts(t)=t3−4t2+2t.
Complete the above, save them into one .pdf, and upload them when complete.