AP Calculus BC Question 330: Answer and Explanation

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Question: 330

5. Which of the following is an equation of the line tangent to the curve with parametric equations x = 3t2 - 2, y = 2t3 + 2 at the point when t = 1?

  • A. y = 3x2 + 7x
  • B. y = 6x - 2
  • C. y = x
  • D. y = x + 3

Correct Answer: D

Explanation:

The correct answer is (D).

and

, and since

is the slope of the tangent line. At t = 1, x = 1, y = 4, so the point of tangency is (1, 4). Equation of tangent: y - 4 = 1(x - 1) ⇒ y = x + 3.