Linear Approximation of a Function
Main Concept
The linear approximation of a function at a point x is a new function of constant slope (its graph is a straight line), which has the same value and slope as the original function at the point x. If the original function is differentiable, the linear approximation to it will be a good approximation to it at surrounding points. Of course, this approximation is generally better at points closer to the point of approximation.
Adjust the sliders to modify where the derivative is being taken and where we are approximating. Enter a different function in the text box to change the function. For example, try sin(x) or tan(x).
Function:
Error in approximation=
Location of Derivative
Location of Approximation
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