Solving Calculus Word Problems

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When solving calculus word problems, it's important to know that the slope of the tangent line and the slope of the curve are the same thing. Discover how rate of change refers to the derivative with help from a math teacher in this free video on basic math lessons.

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Video Transcript

How does one solve calculus word problems? Hi, I'm Jimmy Chang. I've been teaching college math for nine years, and calculus is a course I've been fortunate to teach for the last few years, and one of the things that students always have trouble with, but they're getting better over the years, has been solving calculus word problems. Now, here are some tips, to show you exactly the kind of things that you will need to do, in terms of word clues, so that you'll know exactly what process the word problem will ask you to entail. Now, often in calculus, you'll be taking the derivative a lot, as well as the anti-derivative, AKA the integral, so here are a few words, to help you solve those word problems, related to calculus. Now, when you first start out on calculus, you're going to find pretty soon, on how to find the derivative, AKA rate of change. Now, here are quite a few words, or phrases that will help you, that will tell you immediately, that you need to take the derivative, as part of solving the problem. Now, if they want you to find the slope of the tangent line, the slope of the curve, those two are synonymous with finding the derivative, because part of the definition of the derivative, is finding the slope of the tangent line. Now, but also derivative is the rate of change. If you're asked to find the rate of change, or if you're given in the context of a problem, that things are changing or increasing or decreasing, that's another clue to write things in derivative notation. If you're asked to find things involving marginal, cost, marginal revenue, marginal profit. Marginal is a rate of change, so that tells you, you also have to find the derivative of the function they give you, and lastly, if you're asked to find the maximum profit, or the maximum area, anything like that involving maximum or minimum, again, part of finding the derivative, enables you to find those maximum and minimum values, so a lot of derivative clues. Now, as for the anti-derivative, you use the anti-derivative, or integrals rather, to find areas and volumes of shapes, so now they're asking you to find a volume or an area, given the function, chances are likely that you'll need to set up, some sort of integral, to solve the problem, so I'm Jimmy Chang, and there are some clues, on how to solve those calculus word problems.


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