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Derivative of a function

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Warm-up lim x-6 x 6 x limit exists = -5/0, limit DOES NOT exist lim x 2 -12x+36 x 1 x 2 -7x+6 =-18, limit exists lim x x 9 9-x

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Definition of the Derivative

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EXAMPLE: Find the derivative of f(x) = 3x 2 - 2x f(x) = [3(x+h) 2 - 2(x+h)] - [3x 2 - 2x] h f(x) = [(3x 2 +6xh + 3h 2 ) - (2x+2h)] - [3x 2 - 2x] h f(x) = 3x 2 +6xh + 3h 2 - 2x - 2h - 3x 2 + 2x h f(x) = 6xh + 3h 2 - 2h h f(x) = h (6x + 3h - 2) h f(x) = (6x + 3h - 2) f(x) = (6x - 2)

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PRACTICE 1. f(x)= 5x- 82. f(x)=-3x f(x)= 12x + 3x f(x) = 4x 2 - 5x 5. f(x) = 2x 2 - x f(x) = -3x 2 + 6x - 8 8x - 54x - 1-6x + 6

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