Question

In lect1-Differentiation..while ascertaing the coordinates for Q point x0 and Δx were used for X coordinates but y did he used f(x0+Δx) for Y coordinates inspite of using y0and Δy??

Answer 1

Hi!
Δx isn't a literal position, but rather, it's the distance Q is from x0 along the x-axis. This is why Δx, "delta x", is also known as the "change in x".

So we know P is at (x0, f(x0)), where f(x0) is also known as y0.
The point Q's x-coordinate is Δx distance away from x0, so its x-coordinate is x0+Δx.
The point Q is actually at (x0+Δx, f(x0+Δx)).

Δy, similarly isn't the y-coordinate of Q, but rather Δy is the distance Q is from P along the y-axis. Δy is "delta y" or the "change in y".
Aside from (x0+Δx, f(x0+Δx)) we can also say Q is at (x0+Δx, y0+Δy).