Worksheet: Extrema of a Function Graph
In this worksheet, we will practice interpreting the minimum and maximum values and the end behavior of a function 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 behavior of the quartic, determine whether the leading coefficient is positive or negative.
- APositive
- BNegative
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 behavior 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?
- APositive
- BNegative
Q5:
Which of the following has the lowest minimum value?
- Aa quadratic function whose graph cuts the -axis at −1 and 2 and cuts the -axis at −4
- B
0 1 2 3 4 5 6 7 6 0 −4 −6 −6 −4 0 6 - C
- D
- E
Q6:
The following is the graph of showing the intersection with a line .
Solve .
- A
- B
- C
- D
- E
Solve .
- A
- B
- C
- D
- E
The solution to the previous part shows that is the minimum value of this function. Use the same idea to find the maximum value and the input that achieves this.
- Amaximum value = 3 at
- Bmaximum value = 9 at
- Cmaximum value = 7 at
- Dmaximum value = 5 at
- Emaximum value = 13 at