`f(x) = (x^2 + 3x)/(x - 4)` Find the second derivative of the function.

Textbook Question

Chapter 2, 2.3 - Problem 96 - 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 + 3x)/(x-4)`

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

`or, f'(x) = [2x^2 + 3x - 8x - 12 - x^2 - 3x]/(x-4)^2`

`or, f'(x) = (x^2 - 8x - 12)/(x-4)^2`

`Now,`

`f''(x) = [(x-4)^2*(2x-8) - (x^2 - 8x - 12)*2*(x-4)]/(x-4)^4`

`or, f''(x) = [2(x-4)^3 - 2(x-4)(x^2-8x-12)]/(x-4)^4`

`or, f''(x) = [2(x-4)^2 - 2(x^2-8x-12)]/(x-4)^3`

`or, f''(x) = [2x^2 + 32 - 16x - 2x^2 + 16x + 24]/(x-4)^3`

`or, f''(x) = 56/(x-4)^3`

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