If a continuous function `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 value is negative, then the equation `f(x)=0` has a root in R. Consider `f(x)= ke^(x)-x`, for all real x where k is a real constant.
The positive value of k for which `ke^(x)-x=0` has only one root is

Options

A. No point
B. One point
C. Two points
D. More than two points

Explanation

To solve the problem, we need to find the positive value of \( k \) for which the equation \( k e^x - x = 0 \) has only one root. Let's go through the steps systematically.

### Step 1: Define the function
We start by defining the function:
\[ f(x) = k e^x - x \]

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