CPM Homework Help : CALC Problem 5-158

Given f(x) = x⁴ − x³: Homework Help ✎
1. Find the equation of the tangent line at (1, 0).
2. Find the equation of the line normal to the tangent at (1, 0).
3. Find all points on f(x) with the same slope as in part (b).

Hint (a):

Use the point-slope formula.

Hint (a):

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

Hint (b):

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

Steps (c):

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).