免费切线斜率计算器
计算曲线在给定点的切线斜率(导数值)。
Slope (f'(x₀))
6.0000
公式
## 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)
计算示例
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
常见问题
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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