gaokao 2020 Q20

gaokao · China · national-III-arts 12 marks Applied differentiation Existence and number of solutions via calculus
Given the function $f ( x ) = x ^ { 3 } - k x + k ^ { 2 }$ .
(1) Discuss the monotonicity of $f ( x )$;
(2) If $f ( x )$ has three zeros, find the range of values for $k$ .
Given the function $f ( x ) = x ^ { 3 } - k x + k ^ { 2 }$ .\\
(1) Discuss the monotonicity of $f ( x )$;\\
(2) If $f ( x )$ has three zeros, find the range of values for $k$ .