Why is x log &#x2061;<!-- ⁡ --> ( x ) convex?According to the definition it mus

Davin Fields

Davin Fields

Answered question

2022-05-26

Why is x log ( x ) convex?
According to the definition it must hold:
( t x + ( 1 t ) y ) log ( t x + ( 1 t ) y ) t x log ( x ) + ( 1 t ) y log ( y )
for all positive x , y and t [ 0 , 1 ]
edit: It is allowed to derive, but i have to prove using the definition.

Answer & Explanation

Fahrleine9m

Fahrleine9m

Beginner2022-05-27Added 11 answers

Since f ( x ) = x log x is C 2 , you can derive twice, and see that
f ( x ) = 1 x > 0.
Despiniosnt

Despiniosnt

Beginner2022-05-28Added 3 answers

Given your name, you should know that a function is convex if its second derivative is positive...

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