Understanding the Function y = x^(2/3)

The video tutorial introduces a new graph, y = x^(2/3), and explores its properties. The teacher explains how to plot points and understand fractional indices. Differentiation is used to analyze the graph's behavior, focusing on limits and derivatives. The concept of a cusp is introduced, highlighting its unique characteristics in graph analysis.

What is the initial step suggested for understanding a new function like y = x^(2/3)?

• Use a calculator

• Ask a friend

• Plot points

• Memorize the formula

What does the power of two-thirds represent in the function y = x^(2/3)?

• Square root of x cubed

• Square of x cubed

• Cube root of x squared

• Cube of x squared

Why is differentiation considered a useful tool in understanding the graph of y = x^(2/3)?

• It eliminates the need for plotting

• It provides exact values

• It helps in finding the slope

• It simplifies the equation

As x approaches infinity, what happens to the derivative of y = x^(2/3)?

• It remains constant

• It approaches infinity

• It becomes undefined

• It approaches zero

What is the behavior of the graph of y = x^(2/3) as x approaches negative infinity?

• It increases indefinitely

• It decreases indefinitely

• It approaches zero

• It remains constant

What does a negative derivative indicate about the graph's behavior?

• The graph is increasing

• The graph is decreasing

• The graph is constant

• The graph is oscillating

What is a cusp in the context of the graph of y = x^(2/3)?

• A point where the graph is undefined

• A point where the graph has a sharp turn

• A point where the graph is flat

• A point where the graph intersects the x-axis

How does the graph of y = x^(2/3) behave near the origin?

• It becomes vertical

• It becomes horizontal

• It forms a loop

• It remains linear

What happens to the graph of y = x^(2/3) as x gets very small?

• It becomes steep

• It disappears

• It flattens out

• It oscillates

Which of the following is a characteristic of a cusp?

• It is a smooth curve

• It is a point of inflection

• It is a sharp point

• It is a horizontal line