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Math Help - Equation of the best quadratic approximation?

  1. #1
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    Equation of the best quadratic approximation?

    I'm not sure what to do for this. Here's the problem:

    "(a) Find the equation of the best quadratic approximation to y=ln(x) at x=1. The best quadratic approximation has the same first and second derivatives as y=ln(x) at x=1.

    (b) Use a computer or calculator to graph the approximation and y=ln(x) on the same set of axes. What do you notice?

    (c) Use your quadratic approximation to calculate approximate values for ln(1.1) and ln(2)"

    Parts b and c, I don't doubt that they'd be easy after getting part a.
    So could someone help me with part a?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Rumor View Post
    I'm not sure what to do for this. Here's the problem:

    "(a) Find the equation of the best quadratic approximation to y=ln(x) at x=1. The best quadratic approximation has the same first and second derivatives as y=ln(x) at x=1.

    (b) Use a computer or calculator to graph the approximation and y=ln(x) on the same set of axes. What do you notice?

    (c) Use your quadratic approximation to calculate approximate values for ln(1.1) and ln(2)"

    Parts b and c, I don't doubt that they'd be easy after getting part a.
    So could someone help me with part a?
    Taylor polynomial:

     <br />
f(x)\approx P_2(x)=f(x_0)+(x-x_0)f'(x_0)+\frac{(x-x_0)^2}{2}f''(x_0)<br />

    CB
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