csat-suneung 2021 Q30

csat-suneung · South-Korea · csat__math-humanities 4 marks Stationary points and optimisation Composite or piecewise function extremum analysis
The function $f ( x )$ is a cubic function with leading coefficient 1, and the function $g ( x )$ is a linear function. Define the function $h ( x )$ as $$h ( x ) = \begin{cases} | f ( x ) - g ( x ) | & ( x < 1 ) \\ f ( x ) + g ( x ) & ( x \geq 1 ) \end{cases}$$ If $h ( x )$ is differentiable on the entire set of real numbers, and $h ( 0 ) = 0$, $h ( 2 ) = 5$, find the value of $h ( 4 )$. [4 points]
The function $f ( x )$ is a cubic function with leading coefficient 1, and the function $g ( x )$ is a linear function. Define the function $h ( x )$ as
$$h ( x ) = \begin{cases} | f ( x ) - g ( x ) | & ( x < 1 ) \\ f ( x ) + g ( x ) & ( x \geq 1 ) \end{cases}$$
If $h ( x )$ is differentiable on the entire set of real numbers, and $h ( 0 ) = 0$, $h ( 2 ) = 5$, find the value of $h ( 4 )$. [4 points]