posted by Anonymous .
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.
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.
"You could construct the tangent at different points..."
"You could construct and plot the magnitude of the tangents at different points..."