What is the second derivative of $f(x)= 3x^(2/3)-x^2$ ?

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Answer 1 · 2017-03-08T08:20:46

$f''(x) = -2(1/(3x^(4/3))+1)$

$f(x) = 3x^(2/3)-x^2$

$f'(x) = 3* 2/3x^(2/3-1) - 2x$ [Power rule]

$= 2x^(-1/3) - 2x$

$f''(x) = 2* -1/3x^(-1/3-1) -2$ [Power rule]

$= -2(1/3x^(-4/3)+1)$

$= -2(1/(3x^(4/3))+1)$

What is the second derivative of f(x)= 3x^(2/3)-x^2f(x)= 3x^(2/3)-x^2?