gaokao 2019 Q6

gaokao · China · national-III-science_gkztc Tangents, normals and gradients Determine unknown parameters from tangent conditions

6. The tangent line to the curve $y = a \mathrm { e } ^ { x } + x \ln x$ at the point $( 1 , a \mathrm { e } )$ has equation $y = 2 x + b$ . Then
A. $a = \mathrm { e } , \quad b = - 1$
B. $a = \mathrm { e } , b = 1$
C. $a = \mathrm { e } ^ { - 1 } , b = 1$
D. $a = \mathrm { e } ^ { - 1 } , b = - 1$

In the ancient Chinese classic ``I Ching'', the concept of ``hexagrams'' is used to describe the changes of all things. They are divided into ``yang'' represented by ``—'' and ``yin'' represented by ``- -''. The figure on the right shows a hexagram. The probability that a randomly selected hexagram has exactly five yang lines is

6. The tangent line to the curve $y = a \mathrm { e } ^ { x } + x \ln x$ at the point $( 1 , a \mathrm { e } )$ has equation $y = 2 x + b$ . Then\\
A. $a = \mathrm { e } , \quad b = - 1$\\
B. $a = \mathrm { e } , b = 1$\\
C. $a = \mathrm { e } ^ { - 1 } , b = 1$\\
D. $a = \mathrm { e } ^ { - 1 } , b = - 1$

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