Stationary Points and Derivatives

This video tutorial explains how to find stationary points on a graph, which occur where the gradient is zero. It covers the types of stationary points: minimum, maximum, and inflection points. The tutorial demonstrates how to find these points using derivatives, with examples involving quadratic and cubic functions. The process involves setting the derivative equal to zero and solving for x, then substituting back to find the y-coordinate.

What is a stationary point on a graph?

• A point where the gradient is zero

• A point where the graph intersects the x-axis

• A point where the graph intersects the y-axis

• A point where the graph is vertical

Which of the following is a characteristic of a minimum point?

• The graph is increasing at this point

• The graph is horizontal at this point

• The graph is vertical at this point

• The graph is decreasing at this point

How many minimum points are mentioned in the video?

• Four

• Three

• Two

• One

What is a maximum point on a graph?

• A point where the graph is at its lowest

• A point where the graph is vertical

• A point where the graph is horizontal

• A point where the graph is at its highest

How many maximum points are mentioned in the video?

• Two

• One

• Four

• Three

What is a stationary inflection point?

• A point where the graph is horizontal but not a maximum or minimum

• A point where the graph changes from increasing to decreasing

• A point where the graph is vertical

• A point where the graph changes from decreasing to increasing

How many stationary inflection points are mentioned in the video?

• Three

• Two

• Four

• One

What is the first step in finding a stationary point?

• Find the second derivative

• Find the y-intercept

• Set the function equal to zero

• Set the derivative equal to zero

In the example y = x^2 - 2x + 2, what is the x-coordinate of the stationary point?

• 0

• 3

• 1

• 2

In the example y = x^2 - 2x + 2, what is the y-coordinate of the stationary point?

• 1

• 0

• 3

• 2