Using Lagranges mean value theorem, find a point on the curve `y=sqrt(x-2)` defined on the interval [2,3], where the tangent is parallel to the chord joining the end points of the curve.

Explanation

To solve the problem using Lagrange's Mean Value Theorem, we will follow these steps:

### Step 1: Define the function and interval
We are given the function \( y = \sqrt{x - 2} \) defined on the interval \([2, 3]\).

### Step 2: Verify the conditions of the Mean Value Theorem
1. **Continuity**: The function \( y = \sqrt{x - 2} \) is continuous on the closed interval \([2, 3]\) because the square root function is continuous for \( x \geq 2 \).
2. **Differentiability**: The function is differentiable on the open interval \((2, 3)\) because the derivative exists for all \( x > 2 \).
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