Horizontal Tangents of Implicitly Defined Curve (No Calculator)

Question

Find the equation of the horizontal tangent lines to the curve defined by 2x²+3y²=12.

Answer options:

A. x = +/- √6

B. y = +/- 2

C. x = 0

D. y = +/- √6

Answer 1

2x² + 3y² = 12

4x + 6y(dy/dx) = 0

dy/dx = -4x / (6y)

Horizontal tangent when dy/dx = 0. So, -4x = 0. Therefore, x = 0.

When x = 0, we have 2(0)² + 3y² = 12.

y² = 4

So, y = ± 2.

Answer 2

Equatioon is of an ellipse with major axis on the x-axis. (Algebra 2)

Horizontal tangents perependicular to minor axis of ellipse.