Question

The minimum value of $f\left(x\right) = e^{(x^4-x^3+x^2)}$ is

• A. $e$
• B. $-e$
• C. $1$
• D. $-1$

Answer 1

Answer: (C)

$f(x)=e^{\left(x^{4}-x^{3}+x^{2}\right)}, f^{'}(x)=e^{x^{4}-x^{3}+x^{2}}$
$\left(4 x^{3}-3 x^{2}+2 x\right)$
$\Rightarrow f(x)$ is decreasing for $x < 0$,
increasing for $x > 0$.
$\therefore $ Minimum is at $x=0$
Hence, minimum value of
$f(x)=f(0)=e^{0}=1$