How to tell if a function is increasing or decreasing from derivative?
Increasing functions are those functions that increase monotonically within a particular domain, and decreasing functions are those which decrease monotonically within a particular domain. We check for the monotonicity of a function using derivatives within the given domain. Let's find out how.
Answer: If the first derivative of a function is greater than zero in a particular interval, then it is said to be increasing in that interval, and vice-versa for decreasing function.
Let's understand the statement in detail.
Let's take an example of a function f(x) = x3 + x2 + 3x + 2. Let's find its monotonicity in the domain of real positive numbers.
First of all, we find its first derivative.
Hence, f'(x) = 3x2 + 2x + 3.