Understanding Derivative Graph Behavior

The video tutorial explains how to sketch the derivative of a function by analyzing the slope at various points. It identifies where the slope is zero, positive, or negative, and discusses how these slopes change at different rates. The tutorial then demonstrates how to draw the derivative graph, highlighting key points where the slope has peaks and troughs.

What does it mean when the slope of a function is zero?

• The function is increasing.

• The function is decreasing.

• The function is undefined.

• The function has a horizontal tangent.

Where does the derivative function intersect the x-axis?

• At points where the original function is undefined.

• At points where the slope of the original function is zero.

• At points where the original function is decreasing.

• At points where the original function is increasing.

What is the behavior of the derivative function when the slope of the original function is positive?

• The derivative function is undefined.

• The derivative function is at the x-axis.

• The derivative function is above the x-axis.

• The derivative function is below the x-axis.

What happens to the derivative function when the slope of the original function is negative?

• The derivative function is above the x-axis.

• The derivative function is below the x-axis.

• The derivative function is at the x-axis.

• The derivative function is undefined.

How does the slope change from one point to another when it is increasing at an increasing rate?

• The slope decreases.

• The slope increases more rapidly.

• The slope remains constant.

• The slope becomes zero.

What indicates a peak point in the derivative graph?

• A zero slope.

• A change from decreasing to increasing slope.

• A change from increasing to decreasing slope.

• A constant slope.

What is the behavior of the slope when it decreases at a decreasing rate?

• The slope becomes positive.

• The slope becomes zero.

• The slope becomes less negative.

• The slope becomes more negative.

How can you identify a peak point in the derivative graph?

• By finding where the slope is zero.

• By finding where the slope changes from positive to negative.

• By finding where the slope changes from negative to positive.

• By finding where the slope is constant.

What happens to the slope as you move to the left of a peak point?

• The slope remains constant.

• The slope becomes more negative.

• The slope becomes more positive.

• The slope becomes zero.

What happens to the slope as you move to the right of a peak point?

• The slope becomes more positive.

• The slope becomes more negative.

• The slope remains constant.

• The slope becomes zero.