The problem asks to find $f'(a)$, where $f(x) = 2x^2 - 11x - 25$.

First, let's differentiate $f(x)$ with respect to $x$ to find $f'(x)$:

$f(x) = 2x^2 - 11x - 25$

Differentiating term by term:

$f'(x) = \frac{d}{dx}(2x^2) - \frac{d}{dx}(11x) - \frac{d}{dx}(25)$

Using the power rule, we get:

$f'(x) = 4x - 11$

Now, $f'(a)$ would be:

$f'(a) = 4a - 11$

If a specific value of $a$ is provided, you would substitute it into this equation. If the problem simply asks for the general expression, then the final answer is $f'(a) = 4a - 11$.

Would you like more details on the differentiation process, or do you have any other questions?

Here are 5 related questions you could explore:

1. What is $f'(x)$ for any cubic polynomial?
2. How would you find the second derivative $f''(x)$?
3. What is the derivative of $f(x) = 3x^3 + 2x^2 - 5x + 7$?
4. How does the derivative help in finding local maxima and minima of a function?
5. How would you calculate the derivative of a product of two functions?

Tip: Always apply the power rule carefully by lowering the exponent and multiplying by the original exponent to avoid errors!