Question

The functions $y=x{e}^x$ has minimum at $x=A,y=x^3-3x$ has minimum at $x=B$ and $y=2x^3-3x^2-12x+5$ has minimum at $x=C$, then the ascending order of $A,B,C$ is

• A. A, B, C
• B. B, C, A
• C. A, C, B
• D. B, A, C

Answer 1

The correct option is A A, B, C

$y^{\prime }=e^x+x{e}^x$

$y^{\prime }=(1+x)e^x$

$y^{\prime }=0$ at $x=-1$

$y^{\prime }=3x^2-1$

$y^{\prime }=0$ at $x=\pm \frac{1}{\sqrt{3}}$

y is min at $x=-\frac{1}{\sqrt{3}}$

$y^{\prime }=6x^2-6x-12$

$y^{\prime }=6(x^2-x-2)$

$y^{\prime }=0$ at $x=2,-1$

$y^{\prime }>0$ If $x>2$ or $x<-1$

$y^{\prime }<0$ If $xϵ(-1,2)$

y is min at $x=2$