These are my complete notes for Optimization & Related Rates in Differential Calculus.
I color-coded my notes according to their meaning - for a complete reference for each type of note, see here (also available in the sidebar). All of the knowledge present in these notes has been filtered through my personal explanations for them, the result of my attempts to understand and study them from my classes and online courses. In the unlikely event there are any egregious errors, contact me at jdlacabe@berkeley.edu.
Summary of Optimization & Related Rates (Differential Calculus)
?. Optimization & Related Rates.
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Rule .
Strategy for solving Maximum and Minimum Problems:
- Understand what is being said: Identify and underline pertinent info.
- Draw pictures and label important components of the problem, like a sign chart. Choose a variable for a quantity to be maximized or minimized. Write a function in that variable.
- Graph the function. Determine a reasonable domain.
- Identify the Critical Points and endpoints (use the first derivative).
- Solve the mathematical model. Confirm graphically that your solution makes sense.
- Interpret the solution into the problems setting. Make sure it works & makes sense. Complete sentences.
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Rule .
In Related Rates, you cannot plug in the non-constants, until after the derivative is taken.
