gaokao 2011 Q21

gaokao · China · shanghai-arts Exponential Functions Variation and Monotonicity Analysis

21. (Total: 14 points; Part 1: 6 points; Part 2: 8 points) Given the function $f(x) = a \cdot 2^x + b \cdot 3^x$, where constants $a, b$ satisfy $a \cdot b \neq 0$
(1) If $a \cdot b > 0$, determine the monotonicity of function $f(x)$;
(2) If $a \cdot b < 0$, find the range of $x$ when $f(x+1) > f(x)$.

(12 marks) Given the function $f ( x ) = \frac { a \ln x } { x + 1 } + \frac { b } { x }$, the tangent line to the curve $y = f ( x )$ at the point $( 1 , f ( 1 ) )$ has equation $x + 2 y - 3 = 0$.

21. (Total: 14 points; Part 1: 6 points; Part 2: 8 points)\\
Given the function $f(x) = a \cdot 2^x + b \cdot 3^x$, where constants $a, b$ satisfy $a \cdot b \neq 0$\\
(1) If $a \cdot b > 0$, determine the monotonicity of function $f(x)$;\\
(2) If $a \cdot b < 0$, find the range of $x$ when $f(x+1) > f(x)$.

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23