Analyzing the Function f(x) with Limit Approaches and Derivative Calculations

DESCRIPTION

This text delves into the analysis of the function f(x) = x^2 - 2x using the limit approach to find its derivative. We explore the application of f(3 + h) and calculate the expression, simplifying it to reveal its behavior as h approaches 0. By breaking down the steps, we identify key components such as f(3 + h), f(3), and the resulting limit that leads to the derivative at x = 3. This method illustrates fundamental concepts in calculus, focusing on continuity, differentiability, and the calculation of derivatives through limits.

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May 05, 2026

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Analyzing the Function f(x) with Limit Approaches and Derivative Calculations

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1029 a f(x) = x2 – 2x
1029 a f(x) = x2 – 2x f(3+ h) = (3 +h)2 -2(3+h) f(3+h) = (9+6h+h2) – 6 – 2h f(3+h) = 3+4h+h2
1029 a f(3+h) = 3+4h+h2 f(3) = 32 – 2.3 f(3) = 3 f(3+h) – f(3) = h2 + 4h So