Grade 12 · Math · Calculus

12th grade Tangent lines using derivatives worksheet

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Tangent lines using derivatives

Grade 12 Math Worksheet

NameDate

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

Ari writes the tangent line to f(x) = 12/x at x = 3 as y = mx + b. What is b?
Bo writes the tangent line to f(x) = 20/x at x = 4 as y = mx + b. What is b?
Esme writes the tangent line to f(x) = −6/x at x = 3 as y = mx + b. What is b?
Jun writes the tangent line to f(x) = 15/x at x = 5 as y = mx + b. What is b?
Kira looks for every x where f(x) = x³ − 3x² − 9x + 5 has a horizontal tangent. List them, separated by commas.
Luz looks for every x where f(x) = x³ + 3x² − 24x + 1 has a horizontal tangent. List them, separated by commas.
Milo looks for every x where f(x) = x³ − 9x² + 15x has a horizontal tangent. List them, separated by commas.
8.
Pia finds the tangent line to f(x) = (x + 1)/(x − 1) at x = 2. Which is it?
- y = −2x + 7
- y = −2x − 1
- y = −2x + 3
- y = 2x − 1
9.
Tala finds the tangent line to f(x) = 4/(x² + 1) at x = 1. Which is it?
- y = −2x + 4
- y = −2x
- y = 2x
- y = −2x + 2
10.
Zee finds the tangent line to f(x) = √(2x + 5) at x = 2. Which is it?
- y = (1/3)x + 11/3
- y = 3x − 3
- y = (1/3)x + 7/3
- y = (1/3)x + 3

Tangent lines using derivatives. Every version has 10 questions, and the answer key prints on the second page.

Standard: none (beyond CCSS)

tangent line: The line through (a, f(a)) with slope f′(a).

horizontal tangent: A tangent with slope 0.

parallel: Two lines with the same slope.

Added where the step subtracts. On the tangent line, b = f(a) − f′(a) × a.

Used the height of the point of tangency as the y-intercept. b is the line's height at x = 0.

Swapped the function's value and its slope. The tangent's slope is f′(a); its height at a is f(a).

What is the most common mistake with tangent lines using derivatives?

Added where the step subtracts. On the tangent line, b = f(a) − f′(a) × 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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