Find `f^(')(2)" and "f^(')(5)`, where `f(x)=x^(2)-7x+6`.

Answer

To find \( f'(2) \) and \( f'(5) \) for the function \( f(x) = x^2 - 7x + 6 \), we will follow these steps:

### Step 1: Find the derivative of the function \( f(x) \).

The function given is:
\[ f(x) = x^2 - 7x + 6 \]

To find the derivative \( f'(x) \), we differentiate each term:
- The derivative of \( x^2 \) is \( 2x \).
- The derivative of \( -7x \) is \( -7 \).
- The derivative of the constant \( 6 \) is \( 0 \).

Thus, the derivative is:
\[ f'(x) = 2x - 7 \]

### Step 2: Calculate \( f'(2) \).

Now we will substitute \( x = 2 \) into the derivative:
\[ f'(2) = 2(2) - 7 \]
Calculating this gives:
\[ f'(2) = 4 - 7 = -3 \]

### Step 3: Calculate \( f'(5) \).

Next, we substitute \( x = 5 \) into the derivative:
\[ f'(5) = 2(5) - 7 \]
Calculating this gives:
\[ f'(5) = 10 - 7 = 3 \]

### Final Answers:
\[ f'(2) = -3 \]
\[ f'(5) = 3 \]