To find the equation of the tangent line to the function $f(x)$ at $a = 7$, we follow these steps:

Step 1: Find the value of the function at $x = 7$

The tangent line passes through the point $(7, f(7))$. So, we first calculate $f(7)$.

Step 2: Find the derivative of the function, $f'(x)$

The slope of the tangent line is given by the derivative of the function evaluated at $x = 7$, i.e., $f'(7)$.

Step 3: Use the point-slope form of the equation of a line

The point-slope form of the equation of a tangent line is: $y - f(7) = f'(7)(x - 7)$ Where $(7, f(7))$ is the point of tangency, and $f'(7)$ is the slope.

Could you provide the explicit form of $f(x)$ so I can calculate these values for you?

Would you like details on this process?

Here are some related questions:

1. What is the derivative of a polynomial function?
2. How do you apply the chain rule to find derivatives?
3. What is the geometric interpretation of a tangent line?
4. How can a tangent line be used to approximate function values?
5. How does the derivative at a point relate to the slope of the tangent line?

Tip: The derivative at a point gives the exact slope of the tangent line, which is why it's so useful in calculus!