Work out tangent line instantly with clear inputs, formula shown and shareable results.
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.
Tangent line
y = f(a) + f'(a)(x − a)
f(3) = 9 and f'(3) = 6, giving y = 6x − 9.
It underpins linear approximation, Newton's method and the whole idea of local linearity.