Final answer:
Without a correct function for y, we cannot find the horizontal tangent lines for the equation provided. Normally, we would differentiate the equation with respect to x and set the derivative of y equal to zero to solve for y.
Step-by-step explanation:
To find all the horizontal tangent lines of the graph given by the equation 3x² + 2yt² = 16, we must first differentiate the equation with respect to x, treating y as a function of x (implicit differentiation).
- Differentiate both sides of the equation with respect to x.
- Set the derivative of y with respect to x (dy/dx) to zero since the slope of a horizontal line is 0.
- Solve for y, the points where the horizontal tangents occur.
However, as the given question seems to contain a typo and is missing a clear function definition for y, we cannot provide a precise solution. If the given function were correctly stated, the mentioned steps would be applicable.