csat-suneung 2020 Q12

csat-suneung · South-Korea · csat__math-humanities 3 marks Stationary points and optimisation Determine parameters from given extremum conditions
The function $f ( x ) = - x ^ { 4 } + 8 a ^ { 2 } x ^ { 2 } - 1$ has local maxima at $x = b$ and $x = 2 - 2 b$. What is the value of $a + b$? (Note: $a , b$ are constants with $a > 0 , b > 1$.) [3 points]
(1) 3
(2) 5
(3) 7
(4) 9
(5) 11
The function $f ( x ) = - x ^ { 4 } + 8 a ^ { 2 } x ^ { 2 } - 1$ has local maxima at $x = b$ and $x = 2 - 2 b$. What is the value of $a + b$? (Note: $a , b$ are constants with $a > 0 , b > 1$.) [3 points]\\
(1) 3\\
(2) 5\\
(3) 7\\
(4) 9\\
(5) 11