Grade 12 · Math · Calculus

12th grade Linear approximation worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Linear approximation

Grade 12 Math Worksheet - Building Confidence

NameDate

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

Esme knows f(3) = 10 and f′(3) = 4. Use the tangent line at x = 3 to estimate f(3.2). What is the estimate?
Jun knows f(4) = 7 and f′(4) = −2. Use the tangent line at x = 4 to estimate f(4.3). What is the estimate?
Kira knows f(8) = 20 and f′(8) = 1.5. Use the tangent line at x = 8 to estimate f(8.4). What is the estimate?
Luz knows f(1) = −6 and f′(1) = 3. Use the tangent line at x = 1 to estimate f(0.9). What is the estimate?
5.
Milo wants the linearization of f(x) = √x at x = 9. Which is L(x)?
- L(x) = 9 + (1/6)(x − 3)
- L(x) = 3 + (1/6)(x − 9)
- L(x) = 3 + (1/6)x
6.
Noah wants the linearization of f(x) = x³ at x = 2. Which is L(x)?
- L(x) = 2 + 12(x − 8)
- L(x) = 8 + 12(x − 2)
- L(x) = 8 + 12x
7.
Zee wants the linearization of f(x) = x² at x = 5. Which is L(x)?
- L(x) = 25 + 10x
- L(x) = 25 + 10(x − 5)
- L(x) = 5 + 10(x − 25)
Tala uses the tangent line to y = √x at x = 25 to estimate √26. What is the estimate?
Pia uses the tangent line to y = √x at x = 16 to estimate √17. What is the estimate?
Ari uses the tangent line to y = √x at x = 100 to estimate √104. What is the estimate?

Linear approximation: use the tangent line to estimate a nearby value. Every version has 10 questions, and the answer key prints on the second page.

Standard: none (beyond CCSS)

linearization: The tangent line at a, used as a stand-in for the curve.

step: How far x moves from a: x − a.

overestimate: An estimate bigger than the true value.

Found only slope × step, the change, and did not add the starting value f(a).

Added the slope without multiplying by the step x − a.

Wrote the slope times x instead of times (x − a), so the line misses the point (a, f(a)).

What is the most common mistake with linear approximation?

Found only slope × step, the change, and did not add the starting value f(a).

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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