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Grade 12 · Math

Use a derivative to find a tangent line

Combine a derivative and a point on a quadratic curve to determine a tangent line.

6 authored questions + worked example

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Worked example

For f(x) = x2 + 2, the tangent line at x = 1 is y = 2x + b. What is b?

Answer & why

Answer: 1

The derivative gives slope 2x, or 2 at x = 1. The tangent passes through (1, 3); b = 3 − (2)(1) = 1.

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All questions

All 6 authored questions for this skill.

Question 1

For f(x) = x2 − 1, the tangent line at x = 3 is y = 6x + b. What is b?

  1. -8
  2. -11
  3. -10
  4. -9
A hint

A tangent line uses the derivative for slope and passes through the point on the original curve.

Answer & why

Answer: -10

The derivative gives slope 2x, or 6 at x = 3. The tangent passes through (3, 8); b = 8 − (6)(3) = -10.

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Question 2

For f(x) = x2 + 4, the tangent line at x = -2 is y = -4x + b. What is b?

  1. -1
  2. 0
  3. 2
  4. 1
A hint

A tangent line uses the derivative for slope and passes through the point on the original curve.

Answer & why

Answer: 0

The derivative gives slope 2x, or -4 at x = -2. The tangent passes through (-2, 8); b = 8 − (-4)(-2) = 0.

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Question 3

For f(x) = x2 + 5, the tangent line at x = -3 is y = -6x + b. What is b?

  1. -5
  2. -4
  3. -2
  4. -3
A hint

A tangent line uses the derivative for slope and passes through the point on the original curve.

Answer & why

Answer: -4

The derivative gives slope 2x, or -6 at x = -3. The tangent passes through (-3, 14); b = 14 − (-6)(-3) = -4.

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Question 4

For f(x) = x2 − 2, the tangent line at x = 4 is y = 8x + b. What is b?

  1. -19
  2. -17
  3. -16
  4. -18
A hint

A tangent line uses the derivative for slope and passes through the point on the original curve.

Answer & why

Answer: -18

The derivative gives slope 2x, or 8 at x = 4. The tangent passes through (4, 14); b = 14 − (8)(4) = -18.

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Question 5

For f(x) = x2 + 2, the tangent line at x = 1 is y = 2x + b. What is b?

  1. 1
  2. 0
  3. 2
  4. 3
A hint

A tangent line uses the derivative for slope and passes through the point on the original curve.

Answer & why

Answer: 1

The derivative gives slope 2x, or 2 at x = 1. The tangent passes through (1, 3); b = 3 − (2)(1) = 1.

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Question 6

For f(x) = x2 + 1, the tangent line at x = 2 is y = 4x + b. What is b?

  1. -3
  2. -2
  3. -1
  4. -4
A hint

A tangent line uses the derivative for slope and passes through the point on the original curve.

Answer & why

Answer: -3

The derivative gives slope 2x, or 4 at x = 2. The tangent passes through (2, 5); b = 5 − (4)(2) = -3.

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