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Visualization of a derivative
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Function: y=x^2
Red line: tangent line at a point (1,1)
Blue line: secant line, approaching tangent line
Green line: differential of a function or DY
Magenta line: minor part in the increment of a function or o(deltaX)
Slope: the slope of the secant line.
Derivative is a slope of a tangent line at a point of a curve.
Red dot is an arbitrary fixed point. (1,1)
As we slide second arbitrary point (blue dot) closer to the fixed point, the slope of the secant line approaches the slope of the tangent line.
NOTICE: if the second point reaches the fixed point, we won't be able to calculate rise, run and slope of the secant line, because we need at least two points to do this.
slope of a line: rise/run
dy = derivative * deltaX
o(deltaX) = (dy/deltaX - derivative) * deltaX
Red line: tangent line at a point (1,1)
Blue line: secant line, approaching tangent line
Green line: differential of a function or DY
Magenta line: minor part in the increment of a function or o(deltaX)
Slope: the slope of the secant line.
Derivative is a slope of a tangent line at a point of a curve.
Red dot is an arbitrary fixed point. (1,1)
As we slide second arbitrary point (blue dot) closer to the fixed point, the slope of the secant line approaches the slope of the tangent line.
NOTICE: if the second point reaches the fixed point, we won't be able to calculate rise, run and slope of the secant line, because we need at least two points to do this.
slope of a line: rise/run
dy = derivative * deltaX
o(deltaX) = (dy/deltaX - derivative) * deltaX
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