A negative derivative refers to the rate of change of a function decreasing over a given interval. It is represented by a negative value and indicates that the function is decreasing.
A negative derivative is calculated by finding the slope of a tangent line at a given point on a curve. This can be done by taking the limit of the change in the y-values divided by the change in the x-values as the interval approaches 0.
Graphically, a negative derivative is represented by a downward sloping line on a graph. It indicates that the function is decreasing over the given interval.
Examples of functions with negative derivatives include exponential decay functions, such as y = -2x, and inverse trigonometric functions, such as y = -cos(x).
A negative derivative can be useful in many real-life applications, such as in finance to analyze decreasing trends in stock prices or in physics to calculate the acceleration of a moving object. It also helps to understand and predict changes in natural phenomena, such as population growth and radioactive decay.