1. Section 11.3A Introduction to Derivatives
Tangent line to a graph:
For a line, the slope is always the same. For a curve however, the slope is constantly changing. The tangent line approximates the slope at a given point on the graph of a function.

2. Ex 1: Approximate the slope of f (x) = x2 at (1,1).

3. Secant line:
A secant line is a line that intersects 2 points on the graph of a function.
Think slope:
The tangent line is the value of the slope when
x2 = x1, but this is undefined so we consider the limit of the ratio as x2  x1.

4. Remember slope:
We will let h = x2 – x1, then as x2  x1, h  0.
The slope m of the graph of f at the point (x,f (x)) is equal to the slope of its tangent line at the point and is given by:
provided the limit exists.

5. The slope m of the graph of f at the point (x,f (x))
The slope m of the graph of f at the point (x,f (x)) is equal to the slope of its tangent line at the point and is given by:
provided the limit exists.

6. Ex 3: Find the slope of f (x) = x2 at (-2,4).
Ex 4: Find the formula for the slope of
f (x) = -2x + 4.
Ex 5: Find the formula for the slope of
f (x) = x2 + 1, then find the slope at (-1,2) and (2,5).

7. Suggested Assignment:
Section 11.3A
pg 770
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