Linear Approximation

We need to find the tangent of a given function (such as the curve in the graph, it's y=f(x) here for example) in order to do linear approximation. The tangent line is in red in the graph, marked as y=L(x). By "zooming in" the graph, the tangent and the given function (curve) will overlap each other when x is close enough to a (near x=a), which means in this situation L(x)`~~` f(x). It gives a good approximation near the tangent point a. As x value moves away from a, the approximation will be less and less accurate, so it's important that x must be close enough to a. Here we call the tangent line the linear approximation to function y=f(x) at x=a.  The formula for linear approximation is L(x)=f(a)+f'(a)(x-a).

  • Subject : Math
  • Topic : Calculus
  • Posted By : Jason

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