“If you zoom in enough on non-linear functions they end up looking like linear functions!”
Lets think about circles and its infinite side, the derivative of the non linear function is linear because of its definition of instantaneous slope at one point.(there is no turning point) So, as if there are infinite linear function smaller enough to compose a non linear function.
(Not - hole or the vertex of an a absolute value)
<aside> 💡 The average rate of change of two infinitely close points.
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A tangent line that brushes against the curve at a given point have its slope of the equal to the direction the curve is heading in at that particular point. Therefore, the derivative of a function at a given point is the slope of the tangent line at that point.
However, it is hard to find the slope of the tangent line in a real graph, so secant lines are introduced. The concept of limits and secants mixed. The two points are use to determine the slope of a imaginary line, while as those two points are approaching to the given point; the distance between the two points gets closer and closer as the slope of the two points is approaching closer and closer to the derivative of that given point.
(Forgot the linear slope formula? Click here to review)
Formula/Definiton of Derivative