Tangent Line Equation Formula
Given that the function y = f(x) is differentiable at the point x₀, the equation of the tangent line to the curve at the point (x₀, f(x₀)) is: y - f(x₀) = f'(x…
Syllabus path: Functions › Preliminary Derivatives › Geometric Meaning of Derivative
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CSCA Mathematics Formula Reference
Formula and explanation
Given that the function y = f(x) is differentiable at the point x₀, the equation of the tangent line to the curve at the point (x₀, f(x₀)) is: y - f(x₀) = f'(x₀)(x - x₀) Applicable Condition: The function f(x) is differentiable at x₀. Brief Explanation: This is a direct application of the point - slope form of a line, where the slope is given by the derivative f'(x₀).
Related tutorial and examples
Geometric Meaning of Derivative
Geometric Meaning of Derivative 1. Core Concepts Geometric Meaning: The derivative f'(x₀) of a function y = f(x) at x₀ represents the Slope of the Tangent Line to the curve at the point P(x₀, f(x₀)). k(tangent) = f'(x₀) Visual Intuition: Let P be a fixed point and Q be a moving p…
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