Stationary Points: Finding Maxima and Minima on a Graph

The video tutorial explores the graph of the function y = x^3 - 3x^2, identifying where it crosses the axes and analyzing its gradient. It explains how to find stationary points by differentiating the function and determining the nature of these points as maximum or minimum. The tutorial also covers how to use gradient changes to classify turning points without graphing.

What are the x-coordinates where the graph of y = x^3 - 3x^2 crosses the x-axis?

• 2 and 4

• 1 and 3

• 0 and 3

• 1 and 2

What is the derivative of the function y = x^3 - 3x^2?

• 3x^2 + 6x

• 3x^2 - 6x

• x^2 - 3x

• x^2 + 3x

What are the coordinates of the stationary points for the function y = x^3 - 3x^2?

• (0, 0) and (3, 3)

• (2, 2) and (4, -4)

• (1, 1) and (3, -3)

• (0, 0) and (2, -4)

How can you determine if a turning point is a maximum?

• The gradient remains constant

• The gradient changes from negative to positive

• The gradient changes from positive to negative

• The gradient is zero

What happens to the gradient at a minimum point?

• It becomes undefined

• It remains zero

• It changes from positive to negative

• It changes from negative to positive