gaokao 2024 Q8

gaokao · China · national-II 5 marks Applied differentiation Inequality proof via function study
Let $f ( x ) = ( x + a ) \ln ( x + b )$. If $f ( x ) \geq 0$, then the minimum value of $a ^ { 2 } + b ^ { 2 }$ is
A. $\frac { 1 } { 8 }$
B. $\frac { 1 } { 4 }$
C. $\frac { 1 } { 2 }$
D. 1
Let $f ( x ) = ( x + a ) \ln ( x + b )$. If $f ( x ) \geq 0$, then the minimum value of $a ^ { 2 } + b ^ { 2 }$ is\\
A. $\frac { 1 } { 8 }$\\
B. $\frac { 1 } { 4 }$\\
C. $\frac { 1 } { 2 }$\\
D. 1