Question

Consider the function Maximum value of $f(x)$ occurs at

• A. $x=-\frac{2}{3}$
• B. $x=1$
• C. $x=e^{-2/3}$
• D. $x=e^{2/3}$

Answer 1

Answer: (C)

if $x<e^{-2/3}$ then $f^{\prime }(x)>0$
$x>e^{-2/3}$ then $f^{\prime }(x)<0$
hence $x=e^{-2/3}$ gives local maxima and $x=1$ gives global minima i.e. 0 .