### Home > CALC > Chapter 5 > Lesson 5.5.1 > Problem5-158

5-158.

Given $f(x) = x^4 − x^3$:

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

Use the point-slope formula.

Use $f^\prime(x)$ to find the slope at $x = 1$. You already know the point.

2. Find the equation of the line normal to the tangent at $(1, 0)$.

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

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

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