How to Solve Linear Approximation in Calculus Step by Step

Lesson 13 of the Calculus 1 series: linearization, which uses the derivative to estimate function values near a point where you already know the answer. In this session: The idea: if you know f(x) and f′(x), you can estimate f(x + Δx) for a small Δx Deriving the formula from the definition of the derivative: f(x + Δx) ≈ f(x) + f′(x)·Δx Example 1: how the area of a circle changes when the radius grows from 4 in to 4.02 in Example 2: approximating the cube root of 63.97 from the cube root of 64 (accurate to six decimal places) Example 3: approximating sin(31°) from sin(30°), and why you must convert to radians Example 4: approximating 3.98⁴ from 4⁴ Why the approximation gets worse as Δx grows or as the function gets steeper This builds on the derivative rules from earlier lessons, so watch those first if you haven't yet. Linearization also sets up the later idea of approximating functions with higher derivatives. Questions or something unclear? Drop a comment below. I read and respond to all of them. #Calculus #CalcOne #Linearization #LinearApproximation #Differentials #Derivatives #TangentLineApproximation #MathTutor #LearnCalculus #APCalculus #APCalcAB #APCalcBC #MathAndEngineeringMadeEasy #CalculusForBeginners #STEM