Question

Find any points at which f(x) = x^3 – 3x + 7 has horizontal tangent lines.

A) No horizontal tangent lines exist.
B) x = -1
C) x = 1
D) x = 3

Answer 1

To find points of horizontal tangent lines for the function f(x) = x^3 - 3x + 7, we set the derivative of the function equal to zero. Solving this equation gives x = -1 and x = 1 as the points of horizontal tangency.

Step-by-step explanation:

To find any points at which the function f(x) = x^3 – 3x + 7 has horizontal tangent lines, we need to find the values of x where the derivative of the function is equal to zero. The derivative of f(x) is f'(x) = 3x^2 - 3. Setting this equal to zero and solving for x, we get: 3x^2 - 3 = 0. Factoring out a 3, we have: 3(x^2 - 1) = 0. Setting each factor equal to zero, we find that x = -1 and x = 1. Therefore, the function has horizontal tangent lines at x = -1 and x = 1.