the max value of (1+x)^0.6/(1+x^0.6) in the interval [0, 1] is ? ans :1

When we put the value zero then

(1+x)^0.6=1^0.6=1 and (1+x^0.6)=(1+0^0.6)=1

so (1+x)^0.6/(1+x^0.6)=1/1=1

when we put the value of x=1

(1+1)^0.6/(1+1^0.6)=2^0.6/(1+1)=2^0.6/2=2^(0.6-1)=2^-0.4=1/2^0.4 which is less than 1

now we see that when we put the value zero the answer is greater and when we put the value 1 the answer is less.

this shows that in the interval from 0 to 1 the value of the above expression decreases. Hence the max value is 1.