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Presentation transcript:

Take out a paper and pencil (and eraser) It is now your turn

The graph of f(x) = c is the horizontal line y = c, which has slope 0. examples: The derivative of a constant is zero

(Pascal’s Triangle) We observe a pattern: … power rule examples:

example:

example:

examples:

Inverse:

Example: Remember where we started:

Repeating this procedure at several points, we get the graph shown in this figure. Tangents at x = A, B, and C are horizontal. So, the derivative is 0 there and the graph of f’ crosses the x-axis at those points. Between A and B, the tangents have positive slope. So, f’(x) is positive there. Between B and C, and the tangents have negative slope. So, f’(x) is negative there.

Derivative of a function at a point gives The slope of the tangent line at that point The instantaneous rate of change at that point Application of the Derivative to Motion Then: HOMEWORK 2