brambleberry said:i got y = 2 at first but when i plugged it into the original equation to find x it was impossible to get an answer (the x's canceled out)
rock.freak667 said:the x doesn't cancel out.
4x-2xy=0
2x(2-y)=0
so 2x=0 or 2-y=0.
Meaning x=0,y=2
A horizontal tangent is a line that is parallel to the x-axis and touches the curve of a function at a specific point. This means that the slope of the tangent line at that point is equal to 0.
A horizontal tangent can indicate important information about the behavior of a function. It can help identify maximum or minimum points, points of inflection, and critical points.
To find the horizontal tangent of a function, you need to take the derivative of the function and set it equal to 0. The x-value of the resulting equation will give you the point where the horizontal tangent touches the curve.
Yes, a function can have multiple horizontal tangents. This can occur when the slope of the function changes from positive to 0, then back to positive again.
The horizontal tangent problem can be applied in various real-life situations, such as in physics to determine the maximum height of a projectile or the minimum speed required for a car to make a turn without slipping. It can also be used in economics to find the optimal production level for a business.