By using derivatives, we can find out if a function is an increasing or decreasing function. The increasing function is a function that seems to reach the top of the x-y plane whereas the decreasing function seems like reaching the downside corner of the x-y plane. Let us say we have a function f(x) which is differentiable within the limits (a, b). Then we check any two points on the curve of the function.
- If at any two points x1x1 and x2x2 such that x1x1 < x2x2, there exists a relation f(x1) f(x1) ≤ f(x2)f(x2), then the given function is increasing function in the given interval, and if f(x1)f(x1) < f(x2)f(x2), then the given function is strictly increasing function in the given interval.
- And, if at any two points x1x1 and x2x2 such that x1x1 < x2x2, there exists a relation f(x1)f(x1) ≥ f(x2) f(x2), then the given function is decreasing function in the given interval and if f(x1) f(x1) > f(x2) f(x2), then the given function is strictly decreasing function in the given interval