Question

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

• A. $5$
• B. $1$
• C. $4$
• D. $9$

Answer 1

The correct option is D $9$

$f\left(x\right)=2x^3-9x^2+12x+5f^{\prime }\left(x\right)=6x^2-18x+12=6(x-1)(x-2)f^{\prime }\left(x\right)=0\Rightarrow x=1,2f\left(0\right)=5,f\left(1\right)=10,f\left(2\right)=9,f\left(3\right)=14\Rightarrow M=14\&m=5\therefore M-m=14-5=9$