Exploring Increasing and Decreasing Intervals

What do critical points of a function occur?

• When the function is continuous

• When the function has a maximum value

• When the derivative is zero or does not exist

• When the function is undefined

What does a positive slope of the tangent line indicate about the function?

• The function is constant

• The function is decreasing

• The function has a cusp

• The function is increasing

How do you determine if a function is increasing or decreasing on an interval?

• By analyzing the sign of the first derivative

• By finding the critical points

• By checking the values of the function

• By looking at the sign of the second derivative

What is the first step in determining where a function is increasing or decreasing without a graph?

• Plot the function

• Check the function's continuity

• Find the critical points

• Find the second derivative

If the derivative of a function is negative on an interval, what can be concluded about the function?

• The function is undefined

• The function has a maximum

• The function is decreasing

• The function is increasing

What does a zero value of the derivative at a point usually indicate?

• A cusp

• A point of inflection

• A relative maximum or minimum

• A discontinuity

When given the graph of the derivative, how can you determine where the original function is increasing?

• Where the derivative graph is above the x-axis

• Where the derivative graph is undefined

• Where the derivative graph is below the x-axis

• Where the derivative graph intersects the x-axis

What does it mean if the rate of change of a variable is greater than zero?

• The variable is increasing

• The variable is undefined

• The variable is constant

• The variable is decreasing

In the context of rates of change, what does a negative rate indicate?

• The dependent variable is increasing

• The dependent variable is decreasing

• The independent variable is increasing

• The independent variable is decreasing

How can you show that the number of fruit flies is decreasing at a specific time using the rate of change function?

• By showing the rate of change is negative

• By showing the rate of change is positive

• By showing the rate of change is undefined

• By showing the rate of change is zero