Introduce some simple rules for finding the gradient of a function.
Apply differentiation to identify the maxima and minima of a function.
8.1 Introduction
Calculus—“The mathematics of change”
Calculus is one of the most important discoveries in modern mathematics; questions that were difficult to answer by great mathematicians, scientists, and philosophers for more than two thousand years were solved with the help of Calculus. It is just very advanced algebra and geometry. In one sense, it takes the ordinary rules of algebra and geometry and reforms them to be used on more complicated problems.
The use of Calculus is everywhere, mainly in every branch of science and engineering, business, medicine, etc. The fundamental idea of Calculus is to study change by studying “Instantaneous Change,” which means changes over a short time.
Let’s understand how Calculus is different from simple mathematics. Look at the figure below.
In Figure, Sameer pushes with a constant force for the straight slope, and the crate goes up the slope at a constant speed. With some regular math and simple physics formulas (including algebra and trigonometry), we can calculate the number of calories of energy ...
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