Tangent Line Calculator
Work out tangent line instantly with clear inputs, formula shown and shareable results.
About Tangent Line Calculator
The tangent line touches the curve at a point and matches its slope there, so it is y = f(a) + f'(a)(x − a). It is the best linear approximation to the function near that point.
Formula
Tangent line
y = f(a) + f'(a)(x − a)
Worked example
With the default values below, Tangent Line Calculator returns Tangent line of y = 6x - 9. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Functionone of a·xᵖ, a·sin(kx), a·cos(kx), a·e^(kx), a·ln(kx), a·√(kx)
- a·xᵖ
- Coefficient a
- 1
- Power p or inner coefficient k
- 2
- Point of tangency x
- 3
Results
- Tangent line
- y = 6x - 9
- Slope f'(x)
- 6.00000000
- f(x) at the point
- 9.00000000
- y-intercept
- -9.00000000
Step by step
- 1Values used
- 2Tangent line
- 3Tangent line= y = 6x - 9
- 4Slope f'(x)= 6.00000000
- 5f(x) at the point= 9.00000000
- 6y-intercept= -9.00000000
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Tangent to y = x² at x = 3?
f(3) = 9 and f'(3) = 6, giving y = 6x − 9.
Why is the tangent useful?
It underpins linear approximation, Newton's method and the whole idea of local linearity.