In this section, we examine another application of derivatives: the ability to approximate functions locally by linear functions. Linear functions are the easiest functions with which to work, so …

Local linear approximation is a technique we can use to approximate the values of functions that we’re unable to compute directly. For example, we have no direct way of computing sin (3 4 ∘) …

Local linearity means that if you zoom in really close to a smooth curve at a point, the curve looks like a straight line—specifically its tangent line. So near x = a, f (x) ≈ L (x) = f (a) + f′ (a) (x − a). …

Jan 29, 2025 · Local linearity is a critical concept in both AP Calculus AB and BC, describing how a function behaves like a straight line when examined closely around a specific point. This …

For a differentiable function f(x), the local linear approximation at x = x0 is given by L(x) = f(x0) + f’(x0)(x - x0) Remember: Don’t think of this a formula to be memorized; this is just the tangent …

In multivariable calculus, we extend local linear approximation to derive many important formulas, such as those for multivariable approximation and multivariable chain rule.

x a which gives f(x) f0(a)(x a) + f(a): This is called the linear approximation or tangent line approximation of f at a: The linear function whose graph is this function, that is, L(x) = f(a) + …

Sal introduces the idea of approximating curves using their tangent line equations. This is also called "local linearization."

Sep 23, 2025 · Local Linear Approximation is a method within Differential Calculus designed to simplify complex functions by, quite literally, "zooming in" on them. Instead of grappling with …

Master local linearity and tangent line approximation for the AP Calculus AB/BC exam. Learn how to estimate function values, understand over/underestimates, and practice with examples.