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🗣 Wd提问: cdn加速页面加速

🤖 Ai回答:
cdn 加速页面加速是通过使用 CDN（ content delivery network）技术来 speeds up the load times of web pages、CDN works by distributing the data across multiple data centers around the world, allowing access to the data to be faster for users in different locations、This results in a significant reduction in load times for users, making the web faster and more efficient to use、CDN acceleration is particularly useful for large and complex web pages, such as those with a lot of images or videos, where the load times can be quite long、By offloading some of the data to CDN data centers, the load times for these pages can be significantly reduced、In summary, CDN acceleration pages acceleration works by distributing the data across multiple data centers, allowing access to the data to be faster for users in different locations, resulting in a significant reduction in load times for users.

Given the function \( f(x) = \frac{1}{x^2} \), find the value of \( f(x) \) at \( x = 2 \) and determine the slope of the tangent line to the curve at that point.
To find the value of \( f(x) \) at \( x = 2 \) and the slope of the tangent line to the curve at that point for the function \( f(x) = \frac{1}{x^2} \), we will follow these steps:

1、Evaluate \( f(x) \) at \( x = 2 \):
\[
f(2) = \frac{1}{2^2} = \frac{1}{4}
\]
So, the value of \( f(x) \) at \( x = 2 \) is \( \frac{1}{4} \).

2、Find the derivative \( f'(x) \):
The function \( f(x) = \frac{1}{x^2} \) can be rewritten as \( f(x) = x^{-2} \)、Using the power rule for differentiation, which states that if \( f(x) = x^n \), then \( f'(x) = nx^{n-1} \), we get:
\[
f'(x) = -2x^{-3} = -\frac{2}{x^3}
\]
So, the derivative of \( f(x) \) is \( f'(x) = -\frac{2}{x^3} \).

3、Evaluate the derivative at \( x = 2 \):
\[
f'(2) = -\frac{2}{2^3} = -\frac{2}{8} = -\frac{1}{4}
\]
So, the slope of the tangent line to the curve at \( x = 2 \) is \( -\frac{1}{4} \).

Therefore, the value of \( f(x) \) at \( x = 2 \) is \( \frac{1}{4} \) and the slope of the tangent line to the curve at that point is \( -\frac{1}{4} \)、The final answer is:
\[
\boxed{-\frac{1}{4}}
\]

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