Calcolatore Pendenza della Retta Tangente
Calcola la pendenza della retta tangente a una curva in un punto specifico.
Slope (f'(x₀))
6.0000
Formula
Slope of a Tangent Line
Method
For f(x) = ax^n, the tangent line at x₀ has:
1. Slope = f'(x₀) = a × n × x₀^(n-1) 2. Point = (x₀, f(x₀)) 3. Tangent line equation: y - y₀ = m(x - x₀)
or equivalently: y = mx + (y₀ - mx₀)
Esempio Risolto
Find the tangent line to y = x² at x = 3.
- 01f(3) = 3² = 9, so the point is (3, 9)
- 02f'(x) = 2x, so f'(3) = 6
- 03Tangent line: y - 9 = 6(x - 3)
- 04y = 6x - 9
Domande Frequenti
What is a tangent line?
A tangent line touches a curve at exactly one point and has the same slope as the curve at that point. It represents the best linear approximation of the function near that point.
How is the tangent slope related to the derivative?
The slope of the tangent line at a point is exactly the value of the derivative at that point. The derivative gives the instantaneous rate of change.
What is the normal line?
The normal line is perpendicular to the tangent line. If the tangent slope is m, the normal slope is -1/m.
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