Explanation: First, find the derivative. f ' ( x ) = 3 x 2 + 6 x + 1 A horizontal tangent will have a slope of 0 . The derivative represents the instantaneous rate of change of a function. Set the derivative to 0 and solve for x . 0 = 3 x 2 + 6 x + 1 x = − 6 ± √ 6 2 − 4 ⋅ 3 ⋅ 1 2 ⋅ 3 x = − 6 ± √ 24 6 x = − 6 ± 2 √ 6 6 x = − 1 ± 1 3 √ 6 x = − 3 ± √ 6 Hopefully this helps!
