Gradient of Curves - Differentiation First Principles PDF
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This document details calculations for finding the gradient of a mathematical curve. It demonstrates the process of finding gradients for different values of a variable (x) for a parabolic function (y = 𝑥²). The document also explores whether a clear relationship can be identified between x and the gradient and if a generalized rule for determining the gradient can be established.
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Gradient of Curves - 11/11/24 How do we find the gradient of a curve at a point? Find the gradient of the following curve (𝑦 = 𝑥 ) at: 𝑥 = −3: 𝑥 = −2: 𝑥 = −1: 𝑥 = 0: 𝑥 = 1: 𝑥 = 2: 𝑥 = 3: Can we identify a relationship between 𝑥 and the gradient at that point? Can we extend this to...
Gradient of Curves - 11/11/24 How do we find the gradient of a curve at a point? Find the gradient of the following curve (𝑦 = 𝑥 ) at: 𝑥 = −3: 𝑥 = −2: 𝑥 = −1: 𝑥 = 0: 𝑥 = 1: 𝑥 = 2: 𝑥 = 3: Can we identify a relationship between 𝑥 and the gradient at that point? Can we extend this to find a rule that means we don't have to draw lots of tangents?
