Đồ thị hàm số y=1x+1𝑦=1𝑥+1 không nghịch biến trong các khoảng nào trong các khoảng sau? A. (−1;1)(−1;1) B. (2;4)(2;4) C. (−3;−1)(−3;−1) D. (2;3)(2;3)

To determine the intervals in which the function $y = \frac{1}{x} + 1$ is not monotonically increasing, we should analyze the behavior of the function.

1. Break Down the Problem

We need to find where the function $y = \frac{1}{x} + 1$ is either increasing or decreasing. This is done by examining the derivative of the function.

2. Relevant Concepts

The derivative of a function gives us information about its increasing or decreasing behavior:

• If $f'(x) > 0$, the function is increasing.
• If $f'(x) < 0$, the function is decreasing.

3. Analysis and Detail

1. Find the derivative: $y = \frac{1}{x} + 1$ $\frac{dy}{dx} = -\frac{1}{x^2}$

2. Determine the sign of the derivative: The derivative $\frac{dy}{dx} = -\frac{1}{x^2}$ is negative for all $x \neq 0$. This means the function $y$ is monotonically decreasing everywhere except at $x = 0$ (which is not in the domain).

4. Verify and Summarize

Since $y = \frac{1}{x} + 1$ is always decreasing for $x < 0$ and $x > 0$, it does not become non-decreasing in any of the intervals given.

Final Answer

The function $y = \frac{1}{x} + 1$ is not monotonically increasing in any of the intervals provided. Thus, the answer is none of the options given.