[b]The following applet shows the relationship between the difference quotient of a function f (evaluated from x = a to x = b) and the slope of the secant line (drawn through the graph of the function) connecting the points (a,f(a)) & (b,f(b)). [/b][br][br][color=#0a971e]Feel free to type in any function in the green input box below. [/color][br]You can use the blue slider to adjust the value of [color=#1551b5]a[/color]. (You can also type on in its input box if you wish.) [br]You can use the blue slider to adjust the value of [color=#c51414]b[/color]. (You can also type on in its input box if you wish.)

Questions: [br][br]For any function f that's continuous over the interval [a,b]: [br][br]1) How does the difference quotient of this function relate to the average rate of change of this function? [br]2) How does the difference quotient of this function relate the slope of the secant line connecting (a,f(a)) & (b,f(b))?