If the derivative of a function f(x) is positive for all x in its domain, what c

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Question: If the derivative of a function f(x) is positive for all x in its domain, what can be inferred about the function?

Options:

Correct Answer: The function is increasing.

Solution:

If the derivative of a function is positive for all x, it indicates that the function is increasing throughout its domain.

If the derivative of a function f(x) is positive for all x in its domain, what can be inferred about the function?

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.

Derivative and Function Behavior – Understanding that a positive derivative indicates that the function is increasing.