Find the y-intercept of the tangent line to the curve y = x^3 - 3x + 1 at the point where x = 4.
Answer and explanation
Correct answer: B. -127
- Step 1: The point of tangency is (4, 53). Step 2. Slope = 3x^2 - 3 at x = 4, which is 45. Step 3. The tangent is y - 53 = 45(x - 4), so its y-intercept is 53 - 45 x 4 = -127. Answer: -127. Why not the others: 53: That is the y-coordinate of the point of tangency, not the intercept of the tangent line. 45: That is the slope of the tangent, not its intercept. 127: The sign of the intercept is reversed.
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