1. ## 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.

2. 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
$\displaystyle m_{sec} = \dfrac{f(x + \Delta x) - f(x)}{\Delta x}$

For example, you could let Δx = 0.1 and you would get
$\displaystyle m_{sec} = \dfrac{f(3 + 0.1) - f(3)}{0.1}$
or
$\displaystyle m_{sec} = \dfrac{f(3.1) - f(3)}{0.1}$
Plug in 3 and 3.1 into $\displaystyle f(x) = -x^2 + 4x + 1$ to find f(3) and f(3.1).

After that, pick another value for Δx and repeat.