8d • 🧠 Knowledge
[#1 MATHEMATICS FUN FACT]: DIFFERENTIATION
Differentiation is the process of measuring how fast a function changes. Some of the readers may have learned it in IGCSE Year 2 Maths. This paragraph will explain deeper about how mathematicians developed the idea behind this concept.
On the curve above, point A represents the value of f(x) at x, and point B represents the value of f(x+h) at point (x+h). The straight line (the yellow line) connecting two points A and B is called a secant line. The slope of this line can be calculated by the formula:
Gradient = rise/run:
⇒ f(x+h) - f(x)/(x+h)-x
⇒ f(x+h) - f(x)/h
This secant line represents the average rate of change between the two points A and B. As h becomes smaller (approaches zero), it means that point B gets closer to point A, and the secant line becomes a tangent line. This process gives the exact slope of a curve at a point, which is called the derivative.
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[#1 MATHEMATICS FUN FACT]: DIFFERENTIATION
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