taiwan-gsat 2021 Q7

taiwan-gsat · Other · ast__math-a 8 marks Chain Rule Piecewise Function Differentiability Analysis

Let $F ( x )$ be a polynomial with real coefficients and $F ^ { \prime } ( x ) = f ( x )$ . It is known that $f ^ { \prime } ( x ) > x ^ { 2 } + 1.1$ holds for all real numbers $x$. Select the correct options.
(1) $f ^ { \prime } ( x )$ is an increasing function
(2) $f ( x )$ is an increasing function
(3) $F ( x )$ is an increasing function
(4) $[ f ( x ) ] ^ { 2 }$ is an increasing function
(5) $f ( f ( x ) )$ is an increasing function

Let $F ( x )$ be a polynomial with real coefficients and $F ^ { \prime } ( x ) = f ( x )$ . It is known that $f ^ { \prime } ( x ) > x ^ { 2 } + 1.1$ holds for all real numbers $x$. Select the correct options.\\
(1) $f ^ { \prime } ( x )$ is an increasing function\\
(2) $f ( x )$ is an increasing function\\
(3) $F ( x )$ is an increasing function\\
(4) $[ f ( x ) ] ^ { 2 }$ is an increasing function\\
(5) $f ( f ( x ) )$ is an increasing function

Paper Questions

QA QB QC QI QII Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8