The point on the curve y² = 4x at which the tangent is perpendicular to the line 2x + y = 3 is:

The point on the curve y² = 4x at which the tangent is perpendicular to the line 2x + y = 3 is:

• A. (1, 2)
• B. (4, 4)
• C. (1/4, −1)
• D. (4, −4)

Answer: C) (1/4, −1)

Explanation: Line slope = −2. Tangent slope = 1/2 (perpendicular). dy/dx for y² = 4x is 2y dy/dx = 4 → dy/dx = 2/y. Set 2/y = 1/2 → y = 4. Then 4² = 4x → 16 = 4x → x = 4. Point (4, 4) has tangent slope 2/4 = 1/2. Correct. But option (4, 4) is there. So point (4, 4). Tangent slope = 2/4 = 1/2, which is perpendicular to slope −2. That's correct. But option (1/4, −1) has y = −1, slope = 2/(−1) = −2, not 1/2. So (4, 4) is correct. We'll set correct index to 1.