Use the four-step process to find $$ f^{\prime}(x) $$ and then find $$ f^{\prime}(1), f^{\prime}(5) $$, and $$ f^{\prime}(7) $$. $$ f(x)=2 x^{2}-7 x+5 $$ $$ f^{\prime}(x)=\square $$

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Find the first order derivative with respect to $$ x $$ for $$ 2x^{2}-7x+5 $$.
Evaluate the derivative by following steps:
- step0: Evaluate the derivative:
  $$\frac{d}{dx}\left(2x^{2}-7x+5\right)$$
- step1: Use differentiation rules:
  $$\frac{d}{dx}\left(2x^{2}\right)-\frac{d}{dx}\left(7x\right)+\frac{d}{dx}\left(5\right)$$
- step2: Calculate:
  $$4x-7+0$$
- step3: Remove 0:
  $$4x-7$$
The first derivative of the function $$ f(x) = 2x^{2} - 7x + 5 $$ is $$ f'(x) = 4x - 7 $$.

Now, we need to find the values of $$ f'(1), f'(5), $$ and $$ f'(7) $$ by substituting the respective values of $$ x $$ into the derivative function $$ f'(x) = 4x - 7 $$.

1. $$ f'(1) = 4(1) - 7 = 4 - 7 = -3 $$
2. $$ f'(5) = 4(5) - 7 = 20 - 7 = 13 $$
3. $$ f'(7) = 4(7) - 7 = 28 - 7 = 21 $$

Therefore, $$ f'(1) = -3 $$, $$ f'(5) = 13 $$, and $$ f'(7) = 21 $$.
$$ f'(x) = 4x - 7 $$ $$ f'(1) = -3 $$, $$ f'(5) = 13 $$, $$ f'(7) = 21 $$

Use the four-step process to find and then find , and .

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