Βλέπε Διαφόριση \Τελεστής
y = x^2 and y'(x) = 2x
Graph of a parabola
with a tangent line attached at (1, 1).
the slope is equal to Δy/Δx.
The change in x and y is signed, which indicates whether it is decreasing or increasing.
Before x = 0, x is increasing, and y is decreasing.
Therefore, the slope, which is equal to the derivative, is negative.
This, just, means it is sloping downwards.
The reason the slope graph is linear is
because the slope of the derivative graph represents
how fast the derivative is changing, not the original function.
For a parabola, the derivative changes linearly.
The derivative does not find the points of tangency.
It, just, shows the slope of the tangent lines at the points of the same x coordinate.
A point of tangency is where the tangent line actually meets the graph.
The slope of the tangent, or the derivative, is the slope of its line.
The derivative graph is the value of the slope of the tangent at the point on the parabola with the same x coordinate