Question

How do you know where a function is increasing or decreasing?

A) Evaluate the second derivative
B) Examine the critical points
C) Analyze the slope of the tangent line
D) All of the above

Answer 1

To know where a function is increasing or decreasing, one must evaluate the second derivative, examine the critical points, and analyze the slope of the tangent line.

The Correct Option is; D) All of the above.

Step-by-step explanation:

To determine where a function is increasing or decreasing, it is important to evaluate the second derivative, examine the critical points, and analyze the slope of the tangent line. These methods provide valuable information about the behavior of the function.

1. Evaluating the second derivative helps determine the concavity of the function. If the second derivative is positive, the function is concave up and increasing. If it is negative, the function is concave down and decreasing.
2. Examining the critical points, where the derivative is equal to zero or does not exist, can determine whether the function is increasing or decreasing around those points.
3. Analyzing the slope of the tangent line at various points helps identify where the function is increasing or decreasing. A positive slope indicates an increasing function, while a negative slope indicates a decreasing function.