Let $f (x) = x^4 - x^3$.

1. Write the equation of the tangent line at $(1, 0)$.

   Hint (a):

   Use the Point-Slope formula.

   Hint (a):

   Use $f '(x)$ to calculate the slope at $x = 1$. You already know the point.

2. Write the equation of the line normal to the curve at $(1, 0)$.

   Hint (b):

   Normal lines are means perpendicular to the tangent line at the point of tangency.

3. Find all points on the graph of $y = f (x)$ with the same slope as in part (b).

   Steps (c):

   Let $f\left(x\right) =$ the slope in part (b). Solve for $x$. Then find the corresponding $y$-value(s). Write your answer(s) as coordinate point(s).