In this worksheet, we will practice interpreting the extrema and the end behavior of a given graph.

**Q2: **

Consider the graph of the quartic shown.

Which of the points , , and is a local maximum?

- A
- B
- C

Which of the points , , and is a local minimum?

- A and
- B and
- C and

Which of the points , , and is a global minimum?

- A
- B
- C

By considering the end behaviour of the quartic, determine whether the leading coefficient is positive or negative.

- ANegative
- BPositive

**Q3: **

Consider the cubic graph shown.

What are the coordinates of the local maximum?

- A
- B
- C
- D

What are the coordinates of the local minimum?

- A
- B
- C
- D

If we consider the end behaviour of this cubic, it enters into the bottom left quadrant and exits from the top right quadrant. Is the leading coefficient of this cubic positive or negative?

- ANegative
- BPositive

**Q5: **

Consider a function , where , , and are integers larger than 1. Which of the following statements is true?

- A There will be neither an absolute maximum nor an absolute minimum.
- B If is odd, there will be an absolute maximum.
- C The existence of extremes cannot be determined without more information.
- DIf is even, there will be an absolute minimum.

**Q6: **

Which of the following has the lowest minimum value?

- A
- B
- Ca quadratic function whose graph cuts the -axis at −1 and 2 and cuts the -axis at −4
- D
0 1 2 3 4 5 6 7 6 0 −4 −6 −6 −4 0 6 - E