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Quadratic approximation - Derivative Applications

Quadratic approximation

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Notes:

The formula for quadratic approximation is:

Q(x)=f(a)+f(a)(xa)+f(a)2(xa)2Q(x) = f(a) + f'(a)(x - a) + \frac{f''(a)}{2}(x - a)^{2}

Where:

f(a)+f(a)(xa)f(a) + f'(a)(x - a) is the linear part

f(a)2(xa)2\frac{f''(a)}{2}(x - a)^{2} is the quadratic part.

  • 2.
    Approximating values using Quadratic Approximations

    Find the Quadratic approximation to the function at the given point:

  • 3.
    Consider the function f(x)=xf(x) = \sqrt{x}
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Quadratic approximation

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