If `f(x)=x^(2)-4x+3`, find the value of x for which the derivative is 2.

Answer

To solve the problem, we need to find the value of \( x \) for which the derivative of the function \( f(x) = x^2 - 4x + 3 \) is equal to 2. Let's go through the steps systematically.

### Step 1: Find the derivative of the function
The function is given as:
\[ f(x) = x^2 - 4x + 3 \]
To find the derivative, we apply the power rule:
\[ f'(x) = \frac{d}{dx}(x^2) - \frac{d}{dx}(4x) + \frac{d}{dx}(3) \]
Calculating each term:
- The derivative of \( x^2 \) is \( 2x \).
- The derivative of \( -4x \) is \( -4 \).
- The derivative of a constant (3) is \( 0 \).

Thus, we have:
\[ f'(x) = 2x - 4 \]

### Step 2: Set the derivative equal to 2
We need to find \( x \) such that:
\[ f'(x) = 2 \]
Substituting the expression for the derivative:
\[ 2x - 4 = 2 \]

### Step 3: Solve for \( x \)
Now, we solve the equation:
\[ 2x - 4 = 2 \]
Adding 4 to both sides:
\[ 2x = 2 + 4 \]
\[ 2x = 6 \]
Now, divide both sides by 2:
\[ x = \frac{6}{2} = 3 \]

### Final Answer
Thus, the value of \( x \) for which the derivative is 2 is:
\[ \boxed{3} \]