Wednesday, June 22, 2011

y = f(x)^(1/2)

y' = (1/2)*f(x)^(-1/2)*f'(x)

y'' = (1/2)*(((-1/2)*f(x)^(-3/2)*f'(x)^2)+(f(x)^(-1/2)*f''(x)))

(1/2)*f(x)^(-3/2)*f'(x)^2 = f(x)^(-1/2)*f''(x)

(1/2)*f(x)^(-1)*f'(x)^2 = f''(x)

f(x) = x^3-x

f'(x) = 3*x^2-1

f''(x) = 6*x

(3*x^2-1)^2/(2*x^3-2*x) = 6*x

9*x^4 - 6*x^2 + 1 = 12*x^4 - 12*x^2

6*x^2 + 1 = 3*x^4

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