4-5 Linearization Example

An example of linearization is provided - the approximation of the square root function evaluated at x = 150.

[MrCBorder]

This method can be used to make linear approximations of any continuous, differentiable function. The issue with finding an approximation of the square root of 0.17 will be determining what point to take as the center of your linearization - most of us don't know perfect squares of numbers less than one like we know for integers. In this case you cannot take the linearization of the function about the point x = 0 because the function is not differentiable there. You could use (0.4)^2 = 0.16.