If the derivative of a function f(x) is positive for all x in its domain, what c
Practice Questions
Q1
If the derivative of a function f(x) is positive for all x in its domain, what can be inferred about the function?
The function is decreasing.
The function is constant.
The function is increasing.
The function has a maximum point.
Questions & Step-by-Step Solutions
If the derivative of a function f(x) is positive for all x in its domain, what can be inferred about the function?
Step 1: Understand what a derivative is. The derivative of a function f(x) tells us how the function is changing at any point x.
Step 2: Recognize that if the derivative f'(x) is positive, it means that the function is increasing at that point.
Step 3: Since the derivative is positive for all x in the domain, it means that the function is increasing at every point in its domain.
Step 4: Conclude that if the function is increasing everywhere, it means that as you move from left to right along the x-axis, the values of f(x) are getting larger.
