Derivatives

Apr 2010
25
0
What is the second derivative of f(x) = x-2 / x2 – 3x – 4
I found the first derivative which is f'(x) = -x2 + 4x – 10 / (x2 - 3x – 4)2

When I solve for the second derivative I get f"(x) = (-2x + 4)(x2 - 3x – 4)2 – (-x2 + 4x – 10)(2x - 3)2 / (x2 - 3x – 4)4


When I simplify this though and test it using graphing technology It doesn't equate. What am I doing wrong?
 
Dec 2009
872
381
1111
What is the second derivative of f(x) = x-2 / x2 – 3x – 4
I found the first derivative which is f'(x) = -x2 + 4x – 10 / (x2 - 3x – 4)2

When I solve for the second derivative I get f"(x) = (-2x + 4)(x2 - 3x – 4)2 - (-x2 + 4x – 10)(2x - 3)2 / (x2 - 3x – 4)4


When I simplify this though and test it using graphing technology It doesn't equate. What am I doing wrong?
Dear steezin,

Your the second derivative is incorrect. It should be,

\(\displaystyle f ''(x) = \frac{(-2x + 4)(x^2 - 3x - 4)^2 - ((-x^2 + 4x - 10)\times{2}\times{{\color{red}(x^2-3x-4)}(2x-3)})}{(x^2 - 3x - 4)^4}\)

Hope this will help you.