Month: March 2023

I have been trying to learn Calculus on and off for several years. In the last 3 months I re-read about Limits, Differentiation and Applications of Differentiation and finally, reached the point where I am starting to learn about Integration. It occurred to me that it might be interesting to ...

Every Algebra student knows the distance formula; that is, how to calculate the distance between two points on the Cartesian coordinate plane: \(\boldsymbol{d = \sqrt{\left(x_{2} – x_{1}\right)^{2} + \left(y_{2} – y_{1}\right)^{2}}}\). This week’s blogpost is about finding the distance between a specific point and the closest point(s) in a function. ...

One of the many interesting things I’ve come across while learning calculus is the concept of concavity. A simple example of a concave function is a parabola. The left graph below shows a concave up function: \(\boldsymbol{y = x^{2}}\), while the right graph shows a concave down function: \(\boldsymbol{y = ...

In this post we are going to look at a function and find its minimum value analytically. Instead of just a dry exercise, it is usually more fun to tackle a word problem. All calculus textbooks have several versions of this very same problem. The problem: An is​​land is 3.5 ...

I have used change of variable while trying to solve quadratic equations. Recently, I came across some very clever uses of this technique. Some of the examples below served me as a reminder that it is OK to arbitrarily change the value of one side of an equation… as long ...

Recently I wrote about using the First Derivative (FD) Test to find the intervals where a function is increasing or decreasing. With the FD Test, we can also find the exact value where the function is highest or lowest in an interval (called absolute maxima) or, where it is higher ...