The maximum value of the function f ( x ) = e x + x ln x on the interval 1 ≤ x ≤ 2 is

Question

The maximum value of the function f ( x ) = e x + x ln x on the interval 1 ≤ x ≤ 2 is, e 2 + ln 2 + 1, e 2 + 2 ln 2, e π / 2 + π 2 ln π 2, e 3 / 2 + 3 2 ln 3 2

MARKS App · Accepted Answer

f ' ( x ) = e x + 1 + ln 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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