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$$f:[-5,5]\rightarrow$ is a surjective differentiable function and $g(x)=f(x)f`(x)$ is a twice differentiable function , Given that $g(0)=k$ , find the least integral value of $k$ such that there always existsome $c\in(-5,5)$ for all functions $f(x)$ to satisfy $f`(c)^{2}=-f(c)f``(c)$ and $f(c)^{2}f```(c)<3f`(c)^{3}$

Sarbajit Mazumdar , 6 Years ago

Grade 12

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