To determine if a function has a horizontal tangent line, we calculate the derivative of the function, set it equal to zero, and solve for x. These x-values indicate where the function's slope is zero, meaning there is a horizontal tangent line at those points.
To determine if a function has a horizontal tangent line, we need to look at the derivative of the function. A horizontal tangent line occurs at points where the slope of the curve is zero. Since the slope of the tangent line to a curve at any given point is given by the derivative of the function at that point, we find the horizontal tangent by setting the derivative equal to zero and solving for the variable.
This involves calculating the derivative, setting it equal to zero, and then finding the corresponding x-values. These x-values are where the function has horizontal tangents, provided the function is continuous and differentiable at those points.