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Given: f(x)= 3x^2-5x-9, find f(x+h) - f(x) over h , h cannot equal 0

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ceeee | Student, College Freshman | Honors

Posted March 16, 2012 at 10:53 AM via web

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Given: f(x)= 3x^2-5x-9, find f(x+h) - f(x) over h , h cannot equal 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 16, 2012 at 11:07 AM (Answer #1)

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The function f(x) = 3x^2 - 5x - 9

`(f(x + h) - f(x))/h`

=> `(3(x+h)^2 - 5(x+h) - 9 - (3x^2 - 5x - 9))/h`

=> `(3x^2 + 3h^2 + 6xh - 5x - 5h - 9 - 3x^2 + 5x + 9)/h`

=> `(3h^2 + 6xh - 5h)/h`

=> 3h + 6x - 5

The value of `(f(x + h) - f(x))/h = 3h + 6x - 5`

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