Optimization/Related Rates problems. (General Question)

[Pliffy]

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

 

[rocomath]

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.

 

[nicksauce]

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

 

[dynamicsolo]

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...