Question

The slope of the tangent to the curve (y – x⁵)² = x (1 + x²)² at the point (1, 3) is...

Answer 1

Given curve is (y – x⁵)² = x(1 + x²)²

⇒ 2(y – x⁵) (d/dx – 5x⁴⁾ = (1 + x²)² + 4x(1 + x²)

⇒ 2(y – x5 ) ( dy/dx – 5x⁴) = (1 + x²)(1 + 5x²)

when x = 1, y = 3, then

2(3 – 1) (dy/dx – 5) = (1 + 1)(1 + 5) = 12

⇒ (dy/dx – 5) = 3

⇒ dy/dx = 5 + 3 = 8.

Hence, the slope of the tangent = 8.