If `f` is defined by `f(x)=x^2-4x+7` , show that `f\ '\ (5)=2f\ '(7/2)`

Explanation

To solve the problem, we need to show that \( f'(5) = 2f'\left(\frac{7}{2}\right) \) for the function \( f(x) = x^2 - 4x + 7 \).

### Step 1: Find the derivative \( f'(x) \)

The derivative of a function \( f(x) \) can be found using the limit definition of the derivative:

\[
f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
...