To check if a function is monotonic without using derivatives, you can look for patterns in the function's values. If the function's values consistently increase or decrease as the input increases, then it is monotonic. Another method is to plot the function on a graph and see if it has an overall increasing or decreasing trend.
A monotonic function is a function that either always increases or always decreases as the input increases. In other words, the function's values do not change direction (from increasing to decreasing or vice versa) on any interval of its domain.
No, a function cannot be both increasing and decreasing at different intervals and still be considered monotonic. Monotonicity applies to the entire domain of the function, so if it changes direction at any point, it is not considered monotonic.
The graph of a monotonic function can either have a constantly increasing trend (for a strictly increasing function) or a constantly decreasing trend (for a strictly decreasing function). It will not have any local maximum or minimum points, and the graph will never cross its own curve.
Yes, it is possible for a function to be monotonic but not continuous. Monotonicity only depends on the function's values, while continuity also takes into account the function's behavior at specific points. So, a function can have a consistent increasing or decreasing trend but still have points of discontinuity.