Will you integrate it 2015 times? - VIII

Calculus Level 3

A function $f : \mathbb{R} \rightarrow \mathbb{R}$ is differentiated $2015$ times to get $g(x) = \dfrac{ d^{2015} }{dx^{2015} } \big[ f(x) \big]$ .

True or False

If $g(x)$ is non-negative for all real values of $x$ , then $f(x)$ is a non-decreasing function for all real values of $x$ .

This problem is part of the set - Will you integrate it 2015 times? .

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Guillermo Templado
Dec 16, 2015

Counter example: If $f(x) = x^2$ then g(x) = 0 is non-negative for all real values of x and f(x) is decreasing for x < 0 $\Rightarrow$ the statement above is false

Will you integrate it 2015 times? - VIII

This problem is part of the set - Will you integrate it 2015 times? .

1 solution

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