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The maximum value of the function f(x)=(...

The maximum value of the function `f(x)=((1+x)^(0. 6))/(1+x^(0. 6))` in the interval `[0,1]` is

A

`2^(0.4)`

B

`2^(-0.4)`

C

1

D

`2^(0.6)`

Text Solution

Verified by Experts

The correct Answer is:
3
`f(x) =0.6(1+x)^(0.4)(1+x^(0.6))-0.6x^(0.4)(1+x)^(0.4)/(1+x^(0.6))^(2)`
`=0.6(1+x^(0.6))-x^(0.4(1+x^(1)))/(1+x^(0.6^(2))(1+x^(0.4)))`
`=0.6 (x^(0.4)-1)/(1+x^(0.6^(2)))(1+x)^(0.4)x^(0.4)lt0 forallx in (0,1)`
Hence f(X) is decreasing thus
`f(x)_(max) =f(0)=1`
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