AP Calculus Classes near International City

When I asked several students in International City about their understanding of derivatives, I heard a student say that he knew how to solve them when they were dealing with a textbook problem, but got confused when they had to deal with a problem that involved a changing quantity, like expanding circles, moving objects, or rising water in the AP Calculus problem set.

Amourion's approach to related rates is consistent: if things are changing, state the quantities that are changing; establish the relationship between these quantities; take the derivative with respect to time; and substitute known quantities into the derived equation at the appropriate time.

What are related rates in AP Calculus?

Dr Anil Khare: Related rates are those problems where the rates of change of two or more quantities are related by an equation and where both quantities are variable with time.

Why is it important that students draw diagrams in related-rates problems?

Dr Anil Khare: When at all possible, students should draw figures, as it helps them form a correct maths relation before differentiating.

What are the cases when we should replace numerical values?

Dr Anil Khare: If the variables are changing with time, then numerical values should generally be substituted after differentiation of the relationship.

Why do signs matter in related rates?

Dr Anil Khare: Signs are important because the positive rate indicates a quantity's increase while the negative does its decrease.

How can students be more comfortable with word problems?

To help students get more confident in word problems, they can first convert the contents of the problem into labelled variables and equations before applying calculus.

Turn complicated related-rates descriptions into organised mathematical steps with AP Calculus support from anilkhare.com.