Use differentials to approximate the cube root of 127.

Explanation

To approximate the cube root of 127 using differentials, we can follow these steps:

### Step 1: Define the function
Let \( y = \sqrt[3]{x} \). We want to approximate \( \sqrt[3]{127} \).

### Step 2: Choose a nearby value
We choose a value of \( x \) that is close to 127 and for which we know the cube root. Here, we can take \( x = 125 \) since \( \sqrt[3]{125} = 5 \). Thus, we have:
- \( y = \sqrt[3]{125} = 5 \)
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