Understand the problem
True or False? let \( f : [0,1] \to \Bbb R \) be a continuous function such that \( f(x) \geq x^3\) \(\forall x \in [0,1] \) with \(\int_0^1 f(x)= 1/4 \). Then \( f(x)=x^3 \forall x \in \Bbb R \).
Source of the problem
Start with hints
We know that continuous functions are integrable, so, how can you use this fact to solve this question?
We can see that \( \int_0^1 f(x) dx \geq 1/4 \) but given value is exactly 1/4. Hence we can conclude that \( f(x)=x^3 \).
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