KVPY 2020-21 SB SX Exam Previous Papers

Question : 7 of 120

Marks: +1, -0

The maximum value of the function

f(x)=e^{x}+x \ln x

on the interval

1 \≤ x \≤ 2

Solution:

f'(x)={e}^{{x}}+1+l{n} {x}>0

\;\;

(as

{x} \∈ [1,2])

\⇒f({x})

increases in

[1,2]

\⇒f_{\max }=f(2)={e}^{2}+2 l{n} 2

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