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If the derivative of a function is its slope, then for a constant function, the derivative must be zero. example: The derivative of a constant is zero.

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Presentation on theme: "If the derivative of a function is its slope, then for a constant function, the derivative must be zero. example: The derivative of a constant is zero."— Presentation transcript:

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2 If the derivative of a function is its slope, then for a constant function, the derivative must be zero. example: The derivative of a constant is zero.

3 If we find derivatives with the difference quotient: (Pascal’s Triangle) We observe a pattern: …

4 examples: power rule We observe a pattern:… www.apcalculusbc.com

5 examples: constant multiple rule: When we used the difference quotient, we observed that since the limit had no effect on a constant coefficient, that the constant could be factored to the outside.

6 (Each term is treated separately) constant multiple rule: sum and difference rules:

7 Example: Find the horizontal tangents of: Horizontal tangents occur when slope = zero. Plugging the x values into the original equation, we get: (The function is even, so we only get two horizontal tangents.)

8 www.apcalculusbc.com

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13 First derivative (slope) is zero at: www.apcalculusbc.com

14 product rule: Notice that this is not just the product of two derivatives. This is sometimes memorized as:

15 quotient rule: or

16 Higher Order Derivatives: is the first derivative of y with respect to x. is the second derivative. (y double prime) is the third derivative.is the fourth derivative. We will learn later what these higher order derivatives are used for.  www.apcalculusbc.com


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