AP Calculus/Calculus2A, 2B

Think – Pair – Group Share – Whole class Share

UNIT 2: DERIVATIVES & DIFFERENTIATION

I. DERIVATIVES AND TANGENT LINES (2A, 2B)

A. OBJECTIVE: Find the slope of a tangent line on a curve at a point.

Find the secant line using the given information:

Note:The closer the chosen point is to the given point, the better the approximation gets.

If we want the x-value to get closer and closer to “a”, that means “h” has to get closer and closer to 0.

Materials needed:Whiteboard

Whiteboard marker Eraser

Discuss and use whiteboards:What is the difference between the secant line and tangent line?

What is a Tangent line?

What is the difference between the secant line and tangent line?

Secant line Tangent line

B. All about the Derivative

Finish the sentence:

1. The secant’s slope is the ______________

2. The tangent’s slope is the ________________

Note:

Differentiation is the process.

Derivative is the answer.

(AP Question)Find the equation of the tangent line to the curve that is parallel to the line 4x-2y=3.

Equal your derivative to the slope.

Take out your homework and

your supplies

C. Normal Lines

A normal line is another name for a perpendicular line to the tangent.

Note: The normal slope is -1/ the tangent slope

Homework due Thursday:

Find the derivative with respect to x.

Use complete sentences that include the rules, properties and specific steps that you used.