# Rates of Change

• Aug 2nd 2010, 06:16 PM
ilovemymath
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.
• Aug 2nd 2010, 06:44 PM
eumyang
Quote:

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.