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Paragraph: If a continuous f defined on the real line R , assume positive and negative values in R , then the equation f(x)=0 has a root in R . For example, if it is known that a continuous function f on R is positive at some point and its minimum values is negative, then the equation f(x)=0 has a root in R . Consider f(x)=k e^x-x for all real x , where k is real constant. Question: The line y=x meets y=k e^x for k 0

Options

  1. Ano point
  2. Bone point
  3. Ctwo points
  4. Dmore than two points

Correct answer

B. one point

Step-by-step solution

Let y=x intersect the curve y=k e^x at exactly one point when k 0 .

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