Learn how to generalize the idea of a tangent plane into a linear approximation of scalar-valued multivariable functions.

A "local linearization" is the generalization of tangent plane functions; one that can apply to multivariable functions with any number of inputs.

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

Let h be a differentiable function with h (6) = 2 and h ′ (6) = 1 . What is the value of the approximation of h (6.2) using the function's local linear approximation at x = 6 ?

But there are some functions that we don't see as typically in a algebra or precalculus or calculus class, but it can look like a hard corner from a zoomed out perspective, but as we zoom in once again we'll …

Fundamentally, a local linearization approximates one function near a point based on the information you can get from its derivative (s) at that point. In the case of functions with a two-variable input and …

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Let h be a differentiable function with h (6) = 2 and h ′ (6) = 1 . What is the value of the approximation of h (6.2) using the function's local linear approximation at x = 6 ?

Course: AP®︎/College Calculus AB > Unit 4 Lesson 6: Approximating values of a function using local linearity and linearization Local linearity Local linearity and differentiability Worked example: …