Understanding Derivatives and Graphs

The video tutorial covers evaluating a function at a specific point, sketching and analyzing a parabola, differentiating functions, and solving inequalities. It emphasizes understanding graph features and using derivatives to interpret graph behavior.

What is the result of evaluating the function at x = -3?

• 9

• 12

• 6

• 3

Why is it important to identify key points on a graph?

• To make the graph look nice

• To add more colors to the graph

• To confuse the viewer

• To ensure the graph is unique and accurate

What is the first derivative of the function given in the tutorial?

• 3x

• x^2

• 2x

• x

What is the second derivative of the function?

• 3

• 1

• 2

• 0

What does it mean when a derivative is constant?

• It is independent of x

• It is always negative

• It changes with x

• It is always zero

How do you solve the inequality 2x > 4?

• x < 2

• x > 4

• x > 2

• x = 2

What does a hollow circle on a number line indicate?

• The number is negative

• The number is included

• The number is not included

• The number is zero

What does a negative gradient on a graph indicate?

• The function is increasing

• The function is at a maximum

• The function is decreasing

• The function is constant

What is a stationary point on a graph?

• A point where the function is increasing

• A point where the function is constant

• A point where the tangent is horizontal

• A point where the function is decreasing

What does it mean when the derivative is greater than four?

• The function is decreasing at a rate greater than four

• The function is decreasing rapidly

• The function is increasing at a rate greater than four

• The function is constant