Find the y-intercept of the tangent line to the curve y = x^3 - 3x + 4 at the point where x = 2.
Answer and explanation
Correct answer: D. -12
- Step 1: The point of tangency is (2, 6). Step 2. Slope = 3x^2 - 3 at x = 2, which is 9. Step 3. The tangent is y - 6 = 9(x - 2), so its y-intercept is 6 - 9 x 2 = -12. Answer: -12. Why not the others: 6: That is the y-coordinate of the point of tangency, not the intercept of the tangent line. 9: That is the slope of the tangent, not its intercept. 12: The sign of the intercept is reversed.
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