Question

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 :

• A. 5
• B. 9
• C. 4
• D. 1

Answer 1

Answer: (B)

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