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 \( f(x)=x^3 \forall x \in \Bbb R \).
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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