7 views

Consider the function
$f(x)=x e^{|x|}+4 x^{2}$
for values of $x$ which lie in the interval $[-1,1]$. In this domain, suppose the function attains the minimum value at $x^{*}$. Which of the following is true?

1. $-1 \leq x^{*}<-0.5$
2. $-0.5 \leq x^{*}<0$
3. $x^{*}=0$
4. $0<x^* \leq 0.5$
5. $0.5<x^* \leq 1$