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Let `f,g` and `h` be real-valued functions defined on the interval `[0,1]` by `f(x)=e^(x^2)+e^(-x^2)` , `g(x)=x e^(x^2)+e^(-x^2)` and `h(x)=x^2 e^(x^2)+e^(-x^2)`. if `a,b` and `c` denote respectively, the absolute maximum of `f,g` and `h` on `[0,1]` thenA. `a=b and c ne b`B. `a=c and a ne b`C. `a ne b and c ne b`D. `a=b=c` |
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Answer» Correct Answer - D Given function, `f(x)=x^(x^(2))+e^(-x^(2)),g(x)=xe^(x^(2))+e^(-x^(2)) and h(x)=x^(2)e^(x^(2))+e-x^(2)` are stricctly increasing on [0,1]. Hence, at x=1, the given function, attains absolute maximum all equal to e+1/e. `rArr a=b=c` |
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