How to tell if a function is increasing or decreasing by calculus?

The derivability of a function is nothing but the slope of the function at each point on the graph.

Answer: A function with a positive value of the derivative is increasing and vice versa. 

The slope of a function can either be negative or positive, it cannot be undefined.

Explanation:

Let us suppose a function f(x)

Step 1: Find the derivative of f(x)

Suppose, g(x) is the derivative of f(x), that is, f'(x) = g(x)

Step 2: Check whether the derivative is greater than zero, less than zero or both, in the given domain.

Suppose g(x) > 0 for all domains, thus f(x) can be said to be increasing for all values in the domain.

Suppose g(x) < 0 for all domains, thus f(x) can be said to be decreasing for all values of the domain.

Suppose g(x) > 0 for some part of the domain and g(x) < 0 for other parts of the domain, then f(x) can be said to be partially increasing and partially decreasing function.

Thus, we can tell if a function is increasing or decreasing by looking at the sign of the derivative of the function.