# Visualization of Derivative

- Author:
- Peter Sassman

- Topic:
- 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?