Optimization/Related Rates problems. (General Question)

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In summary, Cal 1 students have difficulty understanding optimization problems on their own. However, if they practice and focus on understanding the problem statement, the calculus operations, and the relationship between the variables, they can usually solve these problems.
  • #1
Pliffy
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Hey guys, i just finished Cal 1 this semester and I am taking Cal 2 next semester. My question is about Optimization and Related rates word problems. In Cal 1 i had a really hard time getting these on my own. I never could seem to get the equation(s) set up 100% correctly. I could easily understand the problems once i had the answer in front of me looking back at them though.

Im wondering if there is any sort of helpfull process to go through when working these problems? I know its very general and I am almost not expecting an actual answer.

Thank you,

-Matt
 
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  • #2
More problems! :-] That's the only way, practice practice practice. When you complete a problem, spend at least 10 minutes reviewing your method; if you look at the solution, spend an additional 10 minutes.

Other than that, you could also go back to Algebra problems to work on "setting" up the problem, it worked for me.
 
  • #3
Optimization:
1) Determine what you're trying to optimize
2) Determine what you can change
3) Find an equation for 1) in terms of 2)
4) Etc.

But really, just practice practice practice
 
  • #4
The related-rates problems generally center on the technique of implicit differentiation. In a lot of those problems, you have two quantities which are connected in some way, but one often needs another variable which does not appear explicitly in order to describe their rates of variation.

The optimization problems in first-semester calculus require finding an "extremum" (maxima or minimum) of some function of a single variable. The information in the problem must be used both to find a function involving the quantity for which this extremum is sought and also to find ways to eliminate all the other variables involved except one. Sometimes the problem provides information that allows the function to be simplified; often, you also need to find from the problem statement a relationship between the variables in the function (what is known as a constraint equation).

Describing this in words makes it sound a lot more complicated than it usually is (at least in Calc-One). The translation of the problem's statement into mathematics sometimes gives students more trouble than carrying out the actual calculus operations...
 

FAQ: Optimization/Related Rates problems. (General Question)

What are optimization problems and why are they important in the field of science?

Optimization problems involve finding the maximum or minimum value of a given function. They are important in science because they help us find the best possible solutions to real-world problems, such as maximizing profits or minimizing costs in business, or finding the most efficient way to design a structure or process in engineering.

How are optimization problems solved?

Optimization problems can be solved using various methods such as calculus, linear programming, or computer algorithms. The specific method used depends on the problem at hand and the available resources.

What are related rates problems and why are they important in science?

Related rates problems involve finding the rate of change of one quantity with respect to another, often using concepts from calculus. They are important in science because they help us understand how different variables are related and how they affect each other in real-world situations.

How are related rates problems solved?

Related rates problems can be solved using calculus techniques such as implicit differentiation and the chain rule. It is important to carefully identify and define all variables and their rates of change in order to set up the appropriate equations.

What are common applications of optimization and related rates problems in science?

Optimization and related rates problems are commonly used in various fields of science such as physics, chemistry, biology, and economics. Some common applications include optimizing the shape and size of objects for maximum strength or efficiency, predicting the spread of diseases, and determining the optimal conditions for chemical reactions.

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