TMUA 2021 Paper 2 Q12 — Worked Solution

P2·Integration, Logic & Quantifiers·6.5Official · 2021 · Q12

definite-integralderivative-inequalitymust-be-true

Which of the following statements about polynomials

f

and

g

is/are true?

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

f (x) \geq g (x)

for all

x \geq 0

, then

f^{'} (x) \geq g^{'} (x)

for all

x \geq 0

III

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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