How does calculus work?

Answer 1

Primarily through differentiation and integration. Differentiation is finding the slope of a function at a specific point. This is the slope of the line that is tangent to that particular point on the line. For instance, an equation of a line may be given as y=2*x+5. We have a y-intercept at 5, and if you've seen this in school, you see that the slope is 2, the number in front of the x. As a child, you are only told to take the number in front of the x, but what they don't tell you is that taking the derivative of this function gives you 2. Notice that in this example, the slope is constant because it's a straight line. The slope is 2 everywhere.

Integration is finding the area under a curve. This is done by adding up little rectangular strips under the curve. Little rectangles may not fit very well under the curve, so when added up, the area will have some error. Integration is a mathematical method of making those little strips infinitely small, so when you add them all up, you don't have any significant error.