In calculus, the derivative of a function is the one that is used to check if the function is increasing or decreasing at any intervals in a given domain. For example, for any given function, y = F (x), if the value of y is increasing while increasing the value of x, then the function is said to be an increasing function, whereas on the other hand, if the value of y is decreasing on increasing the value of x, then it is known as a decreasing function.
In RD Sharma Solutions for Class 12th Maths Chapter 17 increasing and decreasing functions, students solve rational algebraic inequalities. Solving rational algebraic inequalities is nothing but the same as solving polynomial inequalities.
They also get to study strictly increasing functions and strictly decreasing functions. A function is strictly increasing when the y value increases as the x value increases, whereas it is the opposite for strictly decreasing.
Moreover, students also have the opportunity to learn about monotonic functions. A monotonic function is a mathematical function between ordered sets that preserves or reverses the given order. For example, monotonically increasing functions can be considered over an interval on which a function is monotonically increasing output for the function will not occur more than once. In contrast, monotonically decreasing functions are the exact opposite of monotonically increasing functions.
Apart from this, students are taught another topic in monotonic functions, called the necessary and sufficient conditions for monotonicity. Furthermore, they learn how to find the intervals in which a function is increasing or decreasing. They also learn how to prove the monotonicity of a function on a given interval. Lastly, they learn methods to find the interval in which a function is increasing or decreasing.