Google Classroom
GeoGebraGeoGebra Classroom

Visualization of Derivative

The below app shows four different functions, which you can switch by pushing "Switch Function". It also has two points, F and M, and you can move point M using the slider. You can also show the tangent and chords. Play around with the app until you understand the buttons, and then answer the questions below.
Step 1: We want to find the slope of the tangent line, which goes through point F on the function. Push "Show Tangent at F". Step 2: We can easily find the slope between two points, if we have their coordinates. So, if we have a point M, we can draw a chord through the two points, and find the slope. Push "Show Chord Through F and M". Goal: Now, we want to estimate the slope of the tangent line at F, using the chord through F and M. Question 1: By moving point M, how can we make the chord through F and M close to the tangent line through F? Question 2: Try your method for the remaining three functions, by pushing "Switch Function". Does your method still work? Question 3: What happens if we move M to exactly F? Explain why. Question 4: What idea have we learned about recently in math, that uses both your answers to question 2 and 3?