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Manipal MET2010MathematicsApplication of Derivatives

The point in the interval [0,2 ] , where f(x)=e^x x has maximum slope, is

Options

  1. A4
  2. B2
  3. C3 2

Correct answer

B. 2

Step-by-step solution

We have, f(x)=e^x x f^ (x)=e^x x+ x e^x and f^ (x)=- x e^x+ x e^x+ x e^x+ x e^x Now, for maximum or minimum slope put (f^ (x) )^ =0 f^ (x)=0 2 x e^x=0 x=0 x= 2 Also, f^ (x)=-2 x e^x+2 x e^x= negative Slope is maximum at x= / 2 .

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