What is the maximum value of the function f(x)= 1 x+ x , where 0 x 2 ?

Step-by-step solution

f(x)= 1 x+ x = x- x ^2 x+ ^2 x aligned & = 1 2 2 x & f ^ ( x )= 2 x =0 & x = 4 & f ^ ( x )=-2 2 x =-2 4 =-2 0 & f ( x ) is maximum at x = 4 & Maximum value is & f ( 4 )= 1 2 ( 2 )= 1 2 aligned