Tangent Line Approximations

Zoom in until it’s straight

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Tangent line approximation: $f(x) \approx f(a) + f'(a)(x - a)$.
• It works well close to a, and gets worse farther away.
• For small $x$ in radians, $\sin x \approx x$.

Steps

1. Close to the point
2. Estimate a root
3. Compound interest in your head
4. A cube root
5. Dividing without dividing
6. Small angles