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Manipal MET2016MathematicsApplication of Derivatives

If f(x)= ₀^1 e^ |t-x| d t (0 x 1) , then the maximum value of f(x) is

Options

  1. Ae -1
  2. B2(e-1)
  3. C(e-1)
  4. D2( e -1)

Correct answer

C. (e-1)

Step-by-step solution

Given, f(x)= ₀^x e^ |t-x| d t+ _x e^ |t t-x| d t=e^x+e^ 1-x -2 f^ (x)=e^x-e^ 1-x Clearly, x= 1 2 is the point of minima of f(x) . Also, f^ (0)=f(1)=e-1

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