Practice corner: derivatives

Below you have two graphs - if you click on the forward button, at each click you will see the following appear in sequence: 1) on the right hand panel you have a function (appearing in blue), with its equation; then a point on the function; then the tangent line to the function at point , and finally the slope of the tangent line to at point , which is coloured in green. 2) On the left hand panel you have instead a point , then a box where you can input the expression for the derivative of .
1) use your mouse to move point along the graph of and see what happens in the left hand panel - what function is point tracing? 2) insert the expression for the derivative of in the input box in the left hand panel and press enter, so that the function you entered is plotted. How does this relate to the plot traced by point ? 3) Tick the box in the left hand side to reveal the correct expression for the derivative. You can use this applet to insert new functions in the input box in the right hand panel, compute the corresponding derivative in the left hand panel and check whether you have the correct answer. Remember you can always reset the applet by clicking on the reset button in the top right corner.