A horizontal tangent line is a mathematical feature on a graph, located where a function's derivative is zero.
Hence, to find the points on the curve where it has a horizontal tangent line, Find the derivative of the given equation of curve and equate it to zero.
The given equation of curve is:
Find the derivative using implicit differentiation:
Equate the derivative to zero:
Solve the equation:
The solution y=0 does not satisfy the equation of the curve. Hence discard it.
We need to find points on the curve where y=12x.
Hence substitute y=12x into the equation of the curve:
Substitute x=2/6 into the equation of curve:
Notice that y=-2 does not satisfy the equation y=12x for x=1/3.
It follows that the required point is only:
The required point of horizontal tangent line is (1/3, 4).