Determining Function Intervals: Increasing and Decreasing Behavior

Mr. Bean's lesson focuses on determining whether a function is increasing or decreasing using calculus. The video covers identifying critical points, analyzing intervals, and interpreting derivative graphs. It includes example problems and discusses the application of rate of change in real-world scenarios.

What is a critical point in the context of increasing and decreasing functions?

• Where the derivative is zero or does not exist

• Where the function is undefined

• Where the function has a maximum value

• Where the function has a minimum value

How do you determine if a function is increasing in a given interval?

• By checking if the derivative is positive

• By checking if the function is positive

• By checking if the derivative is negative

• By checking if the function is negative

What is the first step in finding the intervals where a function is increasing or decreasing?

• Finding the minimum value

• Finding the second derivative

• Finding the critical points

• Finding the maximum value

In the interval from negative infinity to negative 2, what is the sign of the derivative for the function discussed?

• Undefined

• Zero

• Negative

• Positive

What does a positive derivative indicate about the function in that interval?

• The function is decreasing

• The function is undefined

• The function is constant

• The function is increasing

When using the graph of the derivative, what does it mean if the derivative is above the x-axis?

• The original function is decreasing

• The original function is increasing

• The original function is constant

• The original function is undefined

What is the justification statement for a function increasing on an interval?

• Because the derivative is positive

• Because the derivative is negative

• Because the function is negative

• Because the function is positive

How can you determine if the number of students per year is increasing?

• By checking if the number of students is positive

• By checking if the rate of change is negative

• By checking if the number of students is negative

• By checking if the rate of change is positive

What does a negative rate of change in miles per hour indicate?

• The number of miles is increasing

• The number of miles is decreasing

• The speed is increasing

• The speed is constant

How do you show that the number of flies is decreasing at a specific time?

• By finding the second derivative

• By finding the rate of change and checking if it is negative

• By finding the rate of change and checking if it is positive

• By finding the number of flies and checking if it is negative