Q10
Curve Sketching
Variation Table and Monotonicity from Sign of Derivative
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10. The graph of the function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$ is shown in the figure. Then the correct conclusion is [Figure]
(A) $a > 0 , b < 0 , c > 0 , d > 0$
(B) $a > 0 , b < 0 , c < 0 , d > 0$
(C) $a < 0 , b < 0 , c < 0 , d > 0$
(D) $a > 0 , b > 0 , c > 0 , d < 0$
II. Fill in the Blank Questions
(11) $\lg \frac { 5 } { 2 } + 2 \lg 2 - \left( \frac { 1 } { 2 } \right) ^ { - 1 } =$ $\_\_\_\_$. (12) In $\triangle A B C$, $A B = \sqrt { 6 } , \angle A = 75 ^ { \circ } , \angle B = 45 ^ { \circ }$. Then $A C =$ $\_\_\_\_$. (13) In the sequence $\left\{ a _ { n } \right\}$, $a _ { 1 } = 1 , a _ { n } = a _ { n - 1 } + \frac { 1 } { 2 } ( n \geq 2 )$. Then the sum of the first 9 terms of the sequence $\left\{ a _ { n } \right\}$ equals $\_\_\_\_$. (14) In the rectangular coordinate system $x O y$, if the line $y = 2 a$ and the graph of the function $y = | x - a | - 1$ have only one intersection point, then the value of $a$ is $\_\_\_\_$. (15) $\triangle A B C$ is an equilateral triangle with side length 2. Given that vectors $\vec { a } , \vec { b }$ satisfy $\overrightarrow { A B } = 2 \vec { a } , \overrightarrow { A C } = 2 \vec { a } + \vec { b }$, then the correct conclusions among the following are $\_\_\_\_$. (Write out the serial numbers of all correct conclusions)
(1) $\vec { a }$ is a unit vector; (2) $\vec { b }$ is a unit vector; (3) $\vec { a } \perp \vec { b }$; (4) $\vec { b } \parallel \overrightarrow { B C }$; (5) $( 4 \vec { a } + \vec { b } ) \perp \overrightarrow { B C }$.
III. Solution Questions