Find an equation of a line that is tangent to the graph of f and parallel to the given line.

Question

Function Line

f(x) = x³ 3x − y + 4 = 0

y=__(smaller y-int)

y=__(larger y-int)

Answer 1

f'(x) = 3x² = 3; x = ±1; y = ±1. We have 2 tangent points: (1, 2) and (- 1, - 1) and slope m = 3

Equations of tangent lines: y = 1 + 3(x - 1), y = 3x - 2;

y = - 1 + 3(x + 1); y = 3x + 2.