gaokao 2024 Q16

gaokao · China · national-II Applied differentiation Tangent line computation and geometric consequences
Given function $f ( x ) = \mathrm { e } ^ { x } - a x - a ^ { 3 }$.
(1) When $a = 1$, find the equation of the tangent line to the curve $y = f ( x )$ at the point $( 1 , f ( 1 ) )$;
(2) If $f ( x )$ has a local minimum value that is negative, find the range of values for $a$.
The range of values for $a$ is $(1, +\infty)$. 
Given function $f ( x ) = \mathrm { e } ^ { x } - a x - a ^ { 3 }$.\\
(1) When $a = 1$, find the equation of the tangent line to the curve $y = f ( x )$ at the point $( 1 , f ( 1 ) )$;\\
(2) If $f ( x )$ has a local minimum value that is negative, find the range of values for $a$.
Paper Questions
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