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$f\in C^2([0,1])$$f \in C^2([0,1])$ with $f''$ convex and $f(0)=f'(0)=f''(0)=0$$f(0) = f'(0) = f''(0) = 0$.
Is it true that : $f''(1)+6f(1)\geq 4f'(1)$ ?
Source: AoPS
$f\in C^2([0,1])$ with $f''$ convex and $f(0)=f'(0)=f''(0)=0$.
$f \in C^2([0,1])$ with $f''$ convex and $f(0) = f'(0) = f''(0) = 0$.
