Slope of Tangent Line Calculator
Find the slope and equation of the tangent line to y = ax^n at a given point using the derivative.
Slope (f'(x₀))
6.0000
Y09.0000
Y Intercept-9.0000
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)
Example Calculation
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
Frequently Asked Questions
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