The maximum value of the function $f\left(x\right)=e^x+x\ln x$ on the interval $1\le x\le 2$ is

• A

  $e^2+\ln 2+1$
• Correct answer
  B

  ${\mathrm{e}}^2+2\ln 2$
• C

  ${\mathrm{e}}^{\pi /2}+\frac{\pi }{2}\ln \frac{\pi }{2}$
• D

  ${\mathrm{e}}^{3/2}+\frac{3}{2}\ln \frac{3}{2}$

Hence, the correct answer is option: 'B'.