AP Calculus BC Question 330: Answer and Explanation
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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
The correct answer is (D).
, 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.