Question

Consider the function $f\left(x\right)=2x^3-3x^2$ in the domain $[-1,2].$ The global minimum of $f\left(x\right)$ is

• A. -5

Answer 1

The correct option is A -5
$f\left(x\right)=2x^3-3x^2$ in $xϵ[-1,2]$
$f^{\prime }\left(x\right)=6x^2-6x=0$ (for maxima or minima)
$\Rightarrow x=0$ or $1$
Values of $f\left(x\right)$ at critical points:
$f\left(0\right)=0$
$f\left(1\right)=2-3=-1$
Values of $f\left(x\right)$ at boundaries:
$f(-1)=-2-3=-5$
$f\left(2\right)=16-12=4$
So Global minimum value $-5.$