Section 11.3A Introduction to Derivatives

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Presentation transcript:

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.

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

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.

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.

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.

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).

Suggested Assignment: Section 11.3A pg 770 #1 – 18