Question

help needed!!!
how would you go about drawing the graph of a functions derivative, if the original function is unknown. IE only the graph if F(x) is given but not the equation.

thanks

Answer 1

You could construct the tangent at different points, and if the graph is free of kinks and vertical asymptotes, you can join the different points to get a graph of the derivative.
A kink will imply a discontinuity in the derivative, and a vertical asymptote will mean the same thing in the derivative.
I hope this just about covers most situations.

Answer 2

Addendum:
"You could construct the tangent at different points..."
should read:
"You could construct and plot the magnitude of the tangents at different points..."