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Math Help - Approximate function using first and second derivative?

  1. #1
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    Approximate function using first and second derivative?

    I know how to approximate the value of a function by (a) plugging in values and (b) using a linear approximation, i.e. f(x)\approx f(a)+f'(a)(x-a)

    But, how would one approximate the change in a function, i.e. \Delta y of y=30z+50z^2+40z^3 when z changes from 0.90 to 0.92 by using the first-order and second order derivatives?

    Any insights would be much appreciated!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by horan View Post
    I know how to approximate the value of a function by (a) plugging in values and (b) using a linear approximation, i.e. f(x)\approx f(a)+f'(a)(x-a)

    But, how would one approximate the change in a function, i.e. \Delta y of y=30z+50z^2+40z^3 when z changes from 0.90 to 0.92 by using the first-order and second order derivatives?

    Any insights would be much appreciated!
    You have:

     <br />
f(x+a)=f(x)+a f'(x)+ \frac{a^2}{2} f''(x) + ...<br />

    Hence:

     <br />
f(x+a)-f(x)=a f'(x)+ \frac{a^2}{2} f''(x) + ...<br />

    CB
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