If a graph of a function is given and they tell you to draw the derivative, how do you find it if the function is not given.

Answer 1

draw a tangent line and find the slope of that line, the derivative is equal to the slope of a tangent line at the point

Answer 2

If they want you to PLOT the derivative (df/dx), you will have to measure the slope of the tangent line at a series of points along the f(x) curve, and then plot df/dx vs x.

Answer 3

A triangular plate sits on the x−y plane, and has the following vertices:(0,0), (1,0), and (1,2). It's mass-density is given by the function f(x,y)=xy.