Let `-1lt=plt=1` . Show that the equation `4x^3-3x-p=0` has a unique root in the interval [1/2,1] and identify it.

Explanation

To show that the equation \( 4x^3 - 3x - p = 0 \) has a unique root in the interval \([1/2, 1]\) for \( -1 \leq p \leq 1\), we will follow these steps:

### Step 1: Define the function
Let \( y = 4x^3 - 3x - p \). We need to analyze this function to find the roots.

### Step 2: Differentiate the function
To find the critical points, we differentiate \( y \) with respect to \( x \):
\[
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