gaokao 2024 Q11

gaokao · China · national-II 6 marks Stationary points and optimisation Find critical points and classify extrema of a given function

Let $f ( x ) = 2 x ^ { 3 } - 3 a x ^ { 2 } + 1$. Then
A. When $a > 1$, $f ( x )$ has three zeros
B. When $a < 0$, $x = 0$ is a local maximum point of $f ( x )$
C. There exist $a , b$ such that $x = b$ is an axis of symmetry of the curve $y = f ( x )$
D. There exists $a$ such that the point $( 1 , f ( 1 ) )$ is a center of symmetry of the curve $y = f ( x )$

Let $f ( x ) = 2 x ^ { 3 } - 3 a x ^ { 2 } + 1$. Then\\
A. When $a > 1$, $f ( x )$ has three zeros\\
B. When $a < 0$, $x = 0$ is a local maximum point of $f ( x )$\\
C. There exist $a , b$ such that $x = b$ is an axis of symmetry of the curve $y = f ( x )$\\
D. There exists $a$ such that the point $( 1 , f ( 1 ) )$ is a center of symmetry of the curve $y = f ( x )$

Paper Questions

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