Ali. 2024. “The Emergence of Calculus: A Mathematical Journey of Human Thought.” Medium. Medium. July 20. https://ali.medium.com/the-emergence-of-calculus-a-mathematical-journey-of-human-thought-c7531bdefb90.
Almost fifteen years ago, I found myself nestled by a library window, a spot I still cherish today. It was a rainy day, and I loved watching the raindrops dance against the glass. As I opened my book to where I had paused, one sentence quickly captured my imagination. The author introduced himself as “a curious character” and proclaimed, “I have to understand the world, you see.” This heartfelt statement resonated deeply with me as a young, inquisitive math student. It was such an “Aha” moment for me and it struck me like a lightning bolt, sparking such excitement that I wished I could treat everyone in the library to a cup of tea and engage in lively discussions about the book until dawn.
Ghukasyan, Gohar. “Calculus: The First Derivative Test”. 2022. Medium. https://medium.com/@Gohar_Ghukasyan/calculus-the-first-derivative-test-9898613ceaf5.
In a nutshell, the first derivative test enables us to find increasing and decreasing intervals, critical numbers, and relative extrema.
Ghukasyan, Gohar. “Calculus: The Second Derivative Test”. 2022. Medium. https://medium.com/@Gohar_Ghukasyan/calculus-the-second-derivative-test-31bfa8b1b7a9.
Concavity describes the rate of change of a function’s derivative. If f’ is increasing then the graph is concave up, and if f’ is decreasing, then the graph is concave down. To test for concavity, we have to find the second derivative and determine whether it is positive or negative.
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Mathematical Mysteries 