Let $f(x)=\frac{3 x^{3}}{(4-4 x)^{3}}$. Find the equation of the line tangent to the graph of $f$ at $x=2$. Tangent line: $y=$

Step 1 ：Given the function \(f(x)=\frac{3 x^{3}}{(4-4 x)^{3}}\), we are asked to find the equation of the line tangent to the graph of \(f\) at \(x=2\).

Step 2 ：To find the equation of the tangent line to the graph of a function at a certain point, we need to find the derivative of the function to get the slope of the tangent line at that point.

Step 3 ：The derivative of \(f\) is \(f'(x) = \frac{36x^{3}}{(4 - 4x)^{4}} + \frac{9x^{2}}{(4 - 4x)^{3}}\).

Step 4 ：Evaluating \(f'(2)\), we find that the slope of the tangent line at \(x=2\) is \(\frac{9}{16}\).

Step 5 ：Substituting \(x=2\) into \(f(x)\), we find that the y-coordinate of the point of tangency is \(-\frac{3}{8}\).

Step 6 ：Using the point-slope form of a line, we find that the equation of the tangent line is \(y=\frac{9x}{16} - \frac{3}{2}\).

Step 7 ：\(\boxed{y=\frac{9x}{16} - \frac{3}{2}}\) is the equation of the line tangent to the graph of \(f\) at \(x=2\).