Rate of Change WITHOUT derivatives

PROBLEM: Given f(x)=.04(8x-x²) Find the rate of change of elevation when x = 2 WITHOUT taking a derivatives directly. Instead use find the slope between

The first student should letx = 1 using discussion titleDelta x=1. Then use f(2+1) and f(2-1) tofind the slopebetween two points (1, f(1)) and (3, f(3)). The first line of their post should be The second student should select a different valuex < 1 and find the appropriate f(x+x ) and f(x-x ) to find the slope between two DIFFERENT POINTS closer to the x=2 value.Also include in your title the value of yourx! The third student should select and POST their newx < the second student's value. Again find the new appropriate f(x+x ) and f(x-x ) to find the slope between two DIFFERENT POINTS even closer to the x=2 value. Etc.

When all done, post a comment on at least TWO OTHER STUDENTS' WORK! sec 1.1, pg 47, #3

CHALLENGE: Many students seem to be getting very close to the same answer. Why is that true? Would it be true for any function?