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the max value of (1+x)0.6/(1+x0.6) 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.
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.
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