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JEE Advanced2010MathematicsApplication of DerivativesActual

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] , then

Options

  1. Aa=b and c b
  2. Ba=c and a b
  3. Ca b and c b
  4. Da=b=c

Correct answer

D. a=b=c

Step-by-step solution

Given function, aligned & 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 are strictly aligned increasing on [0,1] . Hence, at x=1 , the given function attains absolute maximum all equal to e+ 1 e . a=b=c

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