Web Reference: Nov 16, 2022 · In this section we discuss using the derivative to compute a linear approximation to a function. We can use the linear approximation to a function to approximate values of the function at certain points. We have seen that linear approximations can be used to estimate function values. They can also be used to estimate the amount a function value changes as a result of a small change in the input. We can use the linear approximation of a function f (x) to find the values of f (x) at the nearest values of a fixed number x = a. The linear approximation is denoted by L (x) and is found using the formula L (x) = f (a) + f ' (a) (x - a), where f ' (a) is the derivative of f (x) at a x = a.
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