Match a function with its derivatives

Grade 12 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

1.
Ari reads the graph of f′ described in the figure. Which must be true about f?
- f is negative for −1 < x < 3
- f has a local max at x = −1 and a local min at x = 3
- f has a local min at x = −1 and a local max at x = 3
- f is 0 at x = −1 and x = 3
2.
Bo reads the graph of f′ described in the figure. Which must be true about f?
- f is 0 at x = −2 and x = 4
- f has a local min at x = 4 and a local max at x = −2
- f is positive for −2 < x < 4
- f has a local max at x = 4 and a local min at x = −2
3.
Esme reads the graph of f′ described in the figure. Which must be true about f?
- f has a local min at x = 1 and a local max at x = 5
- f is 0 at x = 1 and x = 5
- f has a local max at x = 1 and a local min at x = 5
- f is negative for 1 < x < 5
Kira reads the graph of f′ in the figure. What is f″(x)?
Luz reads the graph of f′ in the figure. What is f″(x)?
Milo reads the graph of f′ in the figure. What is f″(x)?
Noah reads the graph of f′ in the figure. What is f″(x)?
8.
f(x) = x³ − 6x². Pia sketches the graph of f″. Which describes it?
- a rising line crossing the x-axis at x = 4
- a falling line crossing the x-axis at x = 2
- a parabola crossing the x-axis at x = 0 and x = 4
- a rising line crossing the x-axis at x = 2
9.
f(x) = x³ + 9x². Ren sketches the graph of f″. Which describes it?
- a rising line crossing the x-axis at x = −3
- a parabola crossing the x-axis at x = 0 and x = −6
- a rising line crossing the x-axis at x = −6
- a falling line crossing the x-axis at x = −3
10.
f(x) = 3x² − x³. Tala sketches the graph of f″. Which describes it?
- a falling line crossing the x-axis at x = 1
- a falling line crossing the x-axis at x = 2
- a parabola crossing the x-axis at x = 0 and x = 2
- a rising line crossing the x-axis at x = 1

Match a function with its derivatives

Answer Key - Grade 12 Math Worksheet

Circle the best answer, or write your answer on the line.

1.
Ari reads the graph of f′ described in the figure. Which must be true about f?
- f is negative for −1 < x < 3
- f has a local max at x = −1 and a local min at x = 3
- f has a local min at x = −1 and a local max at x = 3
- f is 0 at x = −1 and x = 3
2.
Bo reads the graph of f′ described in the figure. Which must be true about f?
- f is 0 at x = −2 and x = 4
- f has a local min at x = 4 and a local max at x = −2
- f is positive for −2 < x < 4
- f has a local max at x = 4 and a local min at x = −2
3.
Esme reads the graph of f′ described in the figure. Which must be true about f?
- f has a local min at x = 1 and a local max at x = 5
- f is 0 at x = 1 and x = 5
- f has a local max at x = 1 and a local min at x = 5
- f is negative for 1 < x < 5
Kira reads the graph of f′ in the figure. What is f″(x)?
3
Luz reads the graph of f′ in the figure. What is f″(x)?
-3
Milo reads the graph of f′ in the figure. What is f″(x)?
5/2
Noah reads the graph of f′ in the figure. What is f″(x)?
2
8.
f(x) = x³ − 6x². Pia sketches the graph of f″. Which describes it?
- a rising line crossing the x-axis at x = 4
- a falling line crossing the x-axis at x = 2
- a parabola crossing the x-axis at x = 0 and x = 4
- a rising line crossing the x-axis at x = 2
9.
f(x) = x³ + 9x². Ren sketches the graph of f″. Which describes it?
- a rising line crossing the x-axis at x = −3
- a parabola crossing the x-axis at x = 0 and x = −6
- a rising line crossing the x-axis at x = −6
- a falling line crossing the x-axis at x = −3
10.
f(x) = 3x² − x³. Tala sketches the graph of f″. Which describes it?
- a falling line crossing the x-axis at x = 1
- a falling line crossing the x-axis at x = 2
- a parabola crossing the x-axis at x = 0 and x = 2
- a rising line crossing the x-axis at x = 1