The slope of the tangent to the curve xy³ − 2x²y² + x⁴ = 0 at the point (1, 1) is:
The slope of the tangent to the curve xy³ − 2x²y² + x⁴ = 0 at the point (1, 1) is:
- A. 1
- B. −1
- C. 0
- D. 2
Answer: A) 1
Explanation: Implicit differentiation: y³ + x·3y² y' − 4xy² − 4x²y y' + 4x³ = 0. At (1, 1): 1 + 3y' − 4 − 4y' + 4 = 0 → (1 − 4 + 4) + (3 − 4)y' = 0 → 1 − y' = 0 → y' = 1.
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