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  4. The maximum value of the function f(x)=2 x3-15 x2+36 x-48 on the set A= x|x2+20 ≤ 9 x| is

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Q. The maximum value of the function $f(x)=2 x^{3}-15 x^{2}+36 x-48$ on the set $A=\left\{x\left|x^{2}+20 \leq 9 x\right|\right\}$ is

JEE AdvancedJEE Advanced 2009

Solution:

$f ^{\prime}( x )=6( x -2)( x -3)$
so $f ( x )$ is increasing $in (3, \infty)$
Also, $A =\{4 \leq x \leq 5\}$
$\therefore f _{\max }= f (5)=7$