Geometrical Interpretation of Differentiation.

When I found the formula of differentiation and by imagining the graph of it I was able to find that the formula gives us the tangent of the curve at the point where the curve is differentiated. Let us discuss about it in detail.

Look at the picture above. We find the when the point Q moves closer and and closer to P along the curve the secant PQ becomes a tangent at P i.e. PT. This happens when  y1 tends to y0 and x1 tends to x0. In graphical terms we write this as y1 → y0 and x1 → x0.When these points becomes very close then the value of y1 − y0 and x1 − x0 becomes infinitely small and y1 − y0 = δ and x1 − x0 = ε. This δ/ε gives the slope of the tangent.

From the previous post,
change in y = Δy and change in x = Δx


This Δy and Δx can be written as δy and δx as the value of both the quantities become infinitely small.



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