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anonymous

  • 5 years ago

find the linearization of f(x) = 1/x at a=10

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  1. anonymous
    • 5 years ago
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    The linearization of a function can be found using the following method: \[f(x) ≈ f(a)+f\prime(a)(x-a)\] Where f(a) = 1/a f'(a) = d/dx(1/a) So, all we have to do is compute the derivative of f(x) and then we have everything we need to get the linearization. \[f(x) = 1/x = x^{-1}\]\[f\prime(x)=-x^{-2}=-1/x^{2}\] Now we just apply the rule to approximate the tangent line at x=a=3 so, \[f\prime(a) = -1/(3)^{2} = -1/9\]\[f(a) = 1/a = 1/3\] Therefore, the linear approximation of f(x) at a = 3 is \[f(x) ≈ 1/3 - 1/9(x - 3)\] Now will you go on a date with me? :P

  2. anonymous
    • 5 years ago
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    haha if your answer turns out to be correct? ;)

  3. anonymous
    • 5 years ago
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    how would i use this to approximate 1/9.78 just plug that in for x?

  4. anonymous
    • 5 years ago
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    Yup, smart and beautiful.

  5. anonymous
    • 5 years ago
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    haha hardly smart if i'm on this thing but thank you

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