Thread: Rates of Change

6)Show a numerical method of approximating the instantaneous rate of change at x = 3 for the function ƒ(x) = -x2 + 4x + 1 using secants. Show two numerical approximations.

7)Show a graphical method of approximating the instantaneous rate of change at x = 3 for the function ƒ(x) = -x2 + 4x + 1 using secants. Show two graphical approximations.

Originally Posted by ilovemymath

6)Show a numerical method of approximating the instantaneous rate of change at x = 3 for the function ƒ(x) = -x2 + 4x + 1 using secants. Show two numerical approximations.

Pick two values of Δx to plug into the difference quotient


For example, you could let Δx = 0.1 and you would get

or

Plug in 3 and 3.1 into to find f(3) and f(3.1).

After that, pick another value for Δx and repeat.