a. For the function and point below, find $f^{\prime}(a)$.
b. Determine an equation of the line tangent to the graph of $f$ at $(a, f(a))$ for the given value of $a$.
\[
f(x)=\frac{3}{\sqrt{x}}, a=\frac{1}{4}
\]

Step 1 ：Given the function \(f(x)=\frac{3}{\sqrt{x}}\) and the point \(a=\frac{1}{4}\).

Step 2 ：First, we need to find the derivative of the function \(f(x)\).

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

Step 4 ：Next, we evaluate the derivative at the point \(a=\frac{1}{4}\).

Step 5 ：Substituting \(a\) into the derivative, we get \(f'(a) = -12\).

Step 6 ：This means the slope of the tangent line at the point \(a\) is -12.

Step 7 ：We also need to find the y-coordinate of the point \((a, f(a))\).

Step 8 ：Substituting \(a\) into the function \(f(x)\), we get \(f(a) = 6\).

Step 9 ：Now we have a point \((a, f(a)) = (\frac{1}{4}, 6)\) and the slope of the tangent line at that point.

Step 10 ：We can use the point-slope form of a line to find the equation of the tangent line.

Step 11 ：The point-slope form of a line is \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is a point on the line.

Step 12 ：Substituting the slope and the point into the equation, we get \(y - 6 = -12(x - \frac{1}{4})\).

Step 13 ：\(\boxed{y - 6 = -12(x - \frac{1}{4})}\) is the equation of the tangent line to the graph of \(f\) at the point \((a, f(a))\).