Which of the following statements about polynomials $f$ and $g$ is/are true? I If $\mathrm { f } ( x ) \geq \mathrm { g } ( x )$ for all $x \geq 0$, then $\int _ { 0 } ^ { x } \mathrm { f } ( t ) \mathrm { d } t \geq \int _ { 0 } ^ { x } \mathrm {~g} ( t ) \mathrm { d } t$ for all $x \geq 0$. II If $\mathrm { f } ( x ) \geq \mathrm { g } ( x )$ for all $x \geq 0$, then $\mathrm { f } ^ { \prime } ( x ) \geq \mathrm { g } ^ { \prime } ( x )$ for all $x \geq 0$. III If $\mathrm { f } ^ { \prime } ( x ) \geq \mathrm { g } ^ { \prime } ( x )$ for all $x \geq 0$, then $\mathrm { f } ( x ) \geq \mathrm { g } ( x )$ for all $x \geq 0$. A none of them B I only C II only D III only E I and II only F I and III only G II and III only H I, II and III
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Which of the following statements about polynomials $f$ and $g$ is/are true?
I If $\mathrm { f } ( x ) \geq \mathrm { g } ( x )$ for all $x \geq 0$, then $\int _ { 0 } ^ { x } \mathrm { f } ( t ) \mathrm { d } t \geq \int _ { 0 } ^ { x } \mathrm {~g} ( t ) \mathrm { d } t$ for all $x \geq 0$.
II If $\mathrm { f } ( x ) \geq \mathrm { g } ( x )$ for all $x \geq 0$, then $\mathrm { f } ^ { \prime } ( x ) \geq \mathrm { g } ^ { \prime } ( x )$ for all $x \geq 0$.
III If $\mathrm { f } ^ { \prime } ( x ) \geq \mathrm { g } ^ { \prime } ( x )$ for all $x \geq 0$, then $\mathrm { f } ( x ) \geq \mathrm { g } ( x )$ for all $x \geq 0$.
A none of them\\
B I only\\
C II only\\
D III only\\
E I and II only\\
F I and III only\\
G II and III only\\
H I, II and III