Calculus 1 — Limits & Derivatives

The tangent line

continues from lesson 2 — values defined earlier in the course stay live here

The derivative buys you the best straight-line approximation at a point: y = f(a) + f′(a)(x − a). At a = 3 that is y = 9 + 6(x − 3) — plotted against the parabola it kisses:

a_{t} = 3

point of tangency

m_{t} = 2 \cdot a_{t}

6

f′(a) by the power rule

f(a_t) + m_t * (x - a_t)

the tangent at x = 3 — compare with the parabola in your head, or change a_t