`f(x) = (x^2 - 4)/(x - 3), c=1` Find f'(x) and f'(c).

Textbook Question

Chapter 2, 2.3 - Problem 15 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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`f(x) = (x^2 - 4)/(x-3)`

`f'(x) = [(x-3)2x - (x^2-4)]/(x-3)^2`

`or, f'(x) = (x^2 - 6x + 4)/(x-3)^2`

`Now, f'(c) = f'(1) = {1^2 - 6*1 + 4}/(1-3)^2`

`or, f'(c) = f'(1) = -1/4`

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