Question

The maximum value of the function $f(x)=e^{x}+x \ln x$ on the interval $1 \leq x \leq 2$ is

• A. $e ^{2}+\ln 2+1$
• B. $e ^{2}+2 \ln 2$
• C. $e ^{\pi / 2}+\frac{\pi}{2} \ln \frac{\pi}{2}$
• D. $e ^{3 / 2}+\frac{3}{2} \ln \frac{3}{2}$

Answer 1

Answer: (B)

$f'(x)=e^{x}+1+\ell n x>0$
(as $x \in[1,2]$)
$\Rightarrow f(x)$ increases in $[1,2]$
$\Rightarrow f_{\max }=f(2)= e ^{2}+2 \ell n 2$