gaokao 2015 Q18

gaokao · China · zhejiang-science Completing the square and sketching Determining coefficients from given conditions on function values or geometry

18. (This question is worth 15 points)
Given the function $f ( x ) = x ^ { 2 } + ax + b$ ( $a , b \in \mathbb{R}$ ), let $M ( a , b )$ denote the maximum value of $| f ( x ) |$ on the interval $[ - 1 , 1 ]$ . (I) Prove that when $| a | \geq 2$ , $M ( a , b ) \geq 2$ ; (II) When $a , b$ satisfy $M ( a , b ) \leq 2$ , find the maximum value of $| a | + | b |$ .

18. (This question is worth 15 points)

Given the function $f ( x ) = x ^ { 2 } + ax + b$ ( $a , b \in \mathbb{R}$ ), let $M ( a , b )$ denote the maximum value of $| f ( x ) |$ on the interval $[ - 1 , 1 ]$ .\\
(I) Prove that when $| a | \geq 2$ , $M ( a , b ) \geq 2$ ;\\
(II) When $a , b$ satisfy $M ( a , b ) \leq 2$ , find the maximum value of $| a | + | b |$ .

Paper Questions

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