TMUA 2021 · Paper 2 · Question 12

Which of the following statements about polynomials $f$ and $g$ is/are true?

I *If* $f (x) \geq g (x)$ for all $x \geq 0$ , *then* $\int_{0}^{x} f (t) d t \geq \int_{0}^{x} g (t) d t$ for all $x \geq 0$ .

II *If* $f (x) \geq g (x)$ for all $x \geq 0$ , *then* $f^{'} (x) \geq g^{'} (x)$ for all $x \geq 0$ .

III *If* $f^{'} (x) \geq g^{'} (x)$ for all $x \geq 0$ , *then* $f (x) \geq g (x)$ for all $x \geq 0$ .

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