Slope of Tangent Line Calculator — 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)
### 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)
Exemplo Resolvido
Find the tangent line to y = x² at x = 3.
- f(3) = 3² = 9, so the point is (3, 9)
- f'(x) = 2x, so f'(3) = 6
- Tangent line: y - 9 = 6(x - 3)
- y = 6x - 9