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derivative of inverse function at point P
Author:
Dick Lane
Topic:
Derivative
Function
is not one-to-one, but restricting its domain can yield a related function G which is one-to-one (and has an inverse function).
Drag points X0 and X1 on x-axis to pick domain for one-to-one function G [plotted using black dashes].
Green curve is reflection of black curve through the line y=x; it is the graph of inverse function
[named Ginv here].
Point P=(a,b) is on the graph of Ginv; you can move P.
Point Q=(b,a) is mirror-image of P on graph of G.
Tangent to G at Q is computed (using derivative of f at b) and displayed.
Slope
of tangent to G at Q is used to compute slope
of tangent to
at P.
Knowing slope of tangent to Ginv at a (i.e., at point P) now lets the tangent to this inverse function to be displayed.
Move P, see how that changes point Q and tangent there to G; also notice the two tangents (at Q and at P) meet at a point on the line y=x.
Function f (and G) can be changed using the input box at bottom of the figure.
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