Find the y-intercept of the tangent line to the curve y = x^3 - 3x + 2 at the point where x = 3.
Answer and explanation
Correct answer: B. -52
- Step 1: The point of tangency is (3, 20). Step 2. Slope = 3x^2 - 3 at x = 3, which is 24. Step 3. The tangent is y - 20 = 24(x - 3), so its y-intercept is 20 - 24 x 3 = -52. Answer: -52. Why not the others: 20: That is the y-coordinate of the point of tangency, not the intercept of the tangent line. 24: That is the slope of the tangent, not its intercept. 52: The sign of the intercept is reversed.
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