a. Find an equation for the line perpendicular to the tangent to the curve $y=x^{3}-4 x+7$ at the point $(2,7)$ b. What is the smallest slope on the curve? At what point on the curve does the curve have this slope? c. Find equations for the tangents to the curve at the points where the slope of the curve is 8 .

Step 1 ：Find the derivative of the function \(y=x^{3}-4 x+7\).

Step 2 ：Evaluate the derivative at the point \((2,7)\) to get the slope of the tangent line.

Step 3 ：The slope of the line perpendicular to the tangent line is the negative reciprocal of the slope of the tangent line.

Step 4 ：Use the point-slope form of the line equation to find the equation of the line.

Step 5 ：The equation of the line perpendicular to the tangent to the curve \(y=x^{3}-4 x+7\) at the point \((2,7)\) is \(\boxed{y = \frac{29}{4} - \frac{x}{8}}\).