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  4. Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f (x)=2x3 - 9x2 + 12x + 5 in the interval [0, 3]. Then M-m is equal to :

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Q. Let $M$ and $m$ be respectively the absolute maximum and the absolute minimum values of the function, $f (x)=2x^3 - 9x^2 + 12x + 5$ in the interval $[0, 3].$ Then $M-m$ is equal to :

JEE MainJEE Main 2018Application of Derivatives

Solution:

Given :
$2 x^{3}-9 x^{2}+12 x+5[0,3] $
$f(0)=2(0)-9(0)+12(0)+5=5 $
$f(1)=2(1)^{3}-9(1)^{2}+12(1)+5 $
$=1-9+12+5=9 $
$f(2)=2(2)^{3}-9(2)^{2}+12(2)+5$
$=16-36+24+5=9 $
$f(3)=2(3)^{3}-9(3)^{2}+12(3)+5 $
$=54-81+36+5=14 $
$f(3)=M=14 $
$f(0)=m=5 $
$M-m \Rightarrow 14-5=9$