A derivative is a mathematical concept that represents the rate of change of a function. It is the slope of a tangent line at a specific point on a curve.
To find the derivative of a function, you can use the power rule, product rule, quotient rule, or chain rule. These are different methods of differentiation that allow you to find the derivative of a function based on its original form.
A horizontal tangent line represents a point on a curve where the slope is equal to zero. This means that the function is not increasing or decreasing at that point, and the tangent line is parallel to the x-axis.
Finding horizontal tangent lines can help you identify critical points of a function, such as maximum and minimum values. It can also help you determine the behavior of a function at a specific point.
Yes, horizontal tangent lines can occur at multiple points on a curve. This can happen when a function has a flat portion or a plateau, where the slope is equal to zero at multiple points.