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NEST2016MathematicsApplication of Derivatives

For a given positive integer n let f:(0, ) R be defined as f(x)=x^n x Then

Options

  1. Af(x) is an increasing function on (0, ) .
  2. Bf has only one zero in (0, ) .
  3. Cf(x) has a minimum at x=1 / [n] e .
  4. Dthe line y=x-1 is a tangent to the graph of f(x) at the point (1,0) .

Correct answer

D. the line y=x-1 is a tangent to the graph of f(x) at the point (1,0) .

Step-by-step solution

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