Drawing Tangents to Curves: quick revision, 8 bites

What is a Tangent?

It's more than just a line!

Takeaway. A tangent 'kisses' the curve at a single point.

Steps to Draw a Tangent

Master this visual skill!

Takeaway. Precision is key: the ruler must only touch at the desired point.

Avoiding Tangent Errors

Don't cross the line!

Takeaway. A true tangent never cuts through the curve at its point of contact.

Tangent's Purpose: Rate of Change

Find instantaneous changes!

The primary application of drawing a tangent is to find the **instantaneous rate of change** of a quantity at a specific point on a curve.

Takeaway. The slope of the tangent reveals how fast something is changing at that exact moment.

Calculating Gradient of a Tangent

Quantify the rate of change!

Takeaway. The gradient calculation uses points *from the tangent line*, not the curve itself.

Instantaneous Speed Example

Speed at a precise moment!

Takeaway. Tangents help us understand motion at specific instants, not just average motion.

Velocity of a Thrown Ball

How fast is it moving *right now*?

Takeaway. From a height-time graph, a tangent's gradient reveals instantaneous vertical velocity.

Practice Makes Perfect

Improve your tangent drawing!

Takeaway. Don't get discouraged; practice is essential for mastering tangent drawing.