1. Tangent Lines & Rates of Change
AP Calculus
September 16, 2016
Mrs. Agnew

2. Essential Stuff Essential Question
How do you find the equation of a tangent line to a curve?
Essential Vocabulary
Secant Line
Tangent line
Instantaneous Rate of Change

3. Tangent Line Problem
From our initial discussion of calculus, we identified two major problems to solve using differentiation:
The Tangent Line Problem
The Velocity Problem
We have examined these problems numerically. We will now solve these problems algebraically using Differential Calculus.

4. The Tangent Line Problem
Line intersects curve at one point
Cannot find slope when given one point
Recall that the slope of a line is the difference in the y values over the difference in the x values.
Using a diagram & secant lines, we can develop a formula for the slope of a tangent line at x = a.

5. Slope of the Tangent Line
The Slope of the Tangent Line at x = a
*The slope of the tangent line is also referred to as the slope of the curve.

6. Examples…
Find the equation of the line tangent to the curve at the point (1, 1).
Find the equation of the line tangent to the curve at the point (1, 3 2 ).
Find the equation of the line tangent to the curve at the point (3, 1).

7. HW: September 16, 2015 Guided Practice Homework (Stewart)
Stewart - page #15, 16, 17, 23(a, b)
Homework (Stewart)
Worksheet on Tangent Lines
Page 148 – 149 #7, 8, 12(a, b), 13, 18, 22(a,b), 25