The maximum value of the function f(x)=e^x+x x on the interval 1 … - Vidyadip

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

✓

Answer

Correct option: B.

$e^2+2 \ln 2$

b
(b)

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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