minimum value of f ( x ) without the use of derivativeAlthough I have solved it using derivative. But did not understand how can i solvewithout derivative, Help Required, Thanks

Question

minimum value of   f  (  x  ) without the use of derivativeAlthough I have solved it using derivative. But did not understand how can i solvewithout derivative, Help Required, Thanks

altaryjny94 · Accepted Answer

Use Young&#039;s inequality.  f  (  x  )  =            x      p        p    +            x              −        q              q    ≥  x  ⋅      1    x    =  1.Since   f  (  1  )  =  1, the minimum is   1

Krish Crosby · Accepted Answer

By AM-GM:            x      p        p    +            x              −        q              q    ≥      1    p    +      1    q    +  x  +      1    x    −  2  ≥      1    p    +      1    q    =  1Since       x    p    −  p  x  +  p  −  1  ≥  0 and       x          −      q        −      q    x    +  q  −  1  ≥  0

Minimum value of f(x)=(x^p)/(p)+(x^(-q))/(q) subjected to 1/p+1/q=1 and p>1 Although I have solved it using derivative. But did not understand how can i solve without derivative, Help Required, Thanks

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