Derivative of Natural Log
The applet below shows the graph of natural log, with a point on it. You can move the point around, using the two sliders. It also shows the slope of the tangent line in green. Move the point around, and then answer the questions below.
Question 1: Push "Plot Slopes", to show all slopes of the function at the given x values. Move the x-coordinate around, to see the slopes plotted. What function do you think is created?
Question 2: Write down the slopes at x=0.25, x=0.5, x=1, x=2, x=4, and x=5. Does this confirm your answer to question 1?
Question 3: In the input bar, graph the equation of your conjecture from question 1, in the form "y=...". Does this confirm your answer to question 1? Make sure the plots are visible.