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Found problems: 1

2008 Gheorghe Vranceanu, 1
Tags: function , inverse calculus , calculus , primitive
Find the $ \mathcal{C}^1 $ class functions $ f:[0,1]\longrightarrow\mathbb{R} $ satisfying the following three clauses: $ \text{(i) } f(0)=0 $ $ \text{(ii) } \text{Im} f'\subset (0,1] $ $ \text{(iii) }F(1)-\frac{\left( f(1) \right)^3}{3} =F(0)=0, $ where $ F $ is a primitive of $ f. $