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Math Help - Rates of Change

  1. #1
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    Rates of Change

    6)Show a numerical method of approximating the instantaneous rate of change at x = 3 for the function (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 (x) = -x2 + 4x + 1 using secants. Show two graphical approximations.
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  2. #2
    Senior Member eumyang's Avatar
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    Quote Originally Posted by ilovemymath View Post
    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
    m_{sec} = \dfrac{f(x + \Delta x) - f(x)}{\Delta x}

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

    After that, pick another value for Δx and repeat.
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