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DERIVATIVE OF A FUNCTION 1.5

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DEFINITION OF A DERIVATIVE OTHER FORMS: OPERATOR:,,,

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DERIVATIVES ****THE DERIVATIVE IS A FUNCTION. IF YOU PLUG IN AN X VALUE, THE DERIVATIVE WILL TELL YOU THE SLOPE OF THE TANGENT LINE AT THAT X VALUE.

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EXAMPLE 1 A)FIND THE DERIVATIVE: B)FIND THE SLOPE OF THE TANGENT LINE AT X=2

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EXAMPLE 2 FIND DY/DX:

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EXAMPLE

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DIFFERENTIABILITY A FUNCTION IS DIFFERENTIABLE EVERYWHERE THAT THE DERIVATIVE EXISTS.

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WHAT IT LOOKS LIKE TO NOT BE DIFFERENTIABLE AT A CORNER AT A CUSP AT A VERTICAL TANGENT AT A DISCONTINUITY

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ONE SIDED DERIVATIVES SHOW THAT THE FOLLOWING FUNCTION IS NOT DIFFERENTIABLE AT X = 0

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APPROXIMATE THE VALUE OF THE DERIVATIVE F(X) F’(1) F’(3) F’(2) F’(-1)

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SKETCHING THE GRAPH GIVEN F(X) GRAPH F’(X)

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HOMEWORK PG 144 #25, 26 ANSWER THE QUESTION AND APPROXIMATE THE VALUE OF F’(X1), F’(X7) PG 156 #1-31 ODD

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Aim: How do we take second derivatives implicitly? Do Now: Find the slope or equation of the tangent line: 1)3x² - 4y² + y = 9 at (2,1) 2)2x – 5y² = -x.

Aim: How do we take second derivatives implicitly? Do Now: Find the slope or equation of the tangent line: 1)3x² - 4y² + y = 9 at (2,1) 2)2x – 5y² = -x.

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