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12th grade Match a function with its derivatives worksheet

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Match a function with its derivatives

Grade 12 Math Worksheet

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  1. Ari reads the graph of f′ described in the figure. Which must be true about f?

    • 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 negative for −1 < 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 max at x = 4 and a local min at x = −2
    • f has a local min at x = 4 and a local max at x = −2
    • f is positive for −2 < x < 4

  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 has a local max at x = 1 and a local min at x = 5
    • f is negative for 1 < x < 5
    • f is 0 at x = 1 and x = 5

  4. Jun reads the graph of f′ described in the figure. Which must be true about f?

    • f has a local min at x = 0 and a local max at x = −4
    • f is positive for −4 < x < 0
    • f is 0 at x = −4 and x = 0
    • f has a local max at x = 0 and a local min at x = −4

  5. Kira reads the graph of f′ in the figure. What is f″(x)?

  6. Luz reads the graph of f′ in the figure. What is f″(x)?

  7. 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 parabola crossing the x-axis at x = 0 and x = 4
    • a rising line crossing the x-axis at x = 4
    • a falling line crossing the x-axis at x = 2
    • 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 rising line crossing the x-axis at x = −6
    • a parabola crossing the x-axis at x = 0 and 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 parabola crossing the x-axis at x = 0 and x = 2
    • a falling line crossing the x-axis at x = 2
    • a falling line crossing the x-axis at x = 1
    • a rising line crossing the x-axis at x = 1
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12th grade Match a function with its derivatives worksheet – printable
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About this worksheet

Matching a function with its derivatives. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can read the sign of f′ from the graph of f, and f's extrema from the graph of f′.
  • I can describe the graphs of f′ and f″ for a polynomial.
  • I can combine the graphs of f′ and f″ to describe f.

Standard: none (beyond CCSS)

Words to know

graph of f′: Its height is f's slope at each x.

turning point: A hilltop or valley, where the derivative is 0.

steepest: Where the slope is largest in size.

Common mistakes

Swapped rising and falling. f′ is positive where f rises and negative where f falls.

Gave the turning points, where f′ = 0, instead of where f′ is negative.

Ran a piece past a turning point of f.

Questions parents ask

What is the most common mistake with match a function with its derivatives?

Swapped rising and falling. f′ is positive where f rises and negative where f falls.

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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