MCQ
The maximum value of the function $f(x)=e^x+x \ln x$ on the interval $1 \leq x \leq 2$ is
- A$e^2+\ln 2+1$
- ✓$e^2+2 \ln 2$
- C$e^{\pi / 2}+\frac{\pi}{2} \ln \frac{\pi}{2}$
- D$e^{3 / 2}+\frac{3}{2} \ln \frac{3}{2}$
Given, $f(x)=e^x+x \ln x$
$f^{\prime}(x)=e^x+1+\ln x>0 \forall x \in(1,2)$
$f(x)$ is increasing.
$\therefore \quad f(x)_{\max }$ at $x=2$
$f(2)=e^2+2 \ln 2$
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