The equation of the horizontal tangent to the curve y = 3x^2 - 14x has to be determined.
The slope of the tangent to a curve f(x) at any point where x = a is given by f'(a). If the tangent is horizontal the slope of the line is 0. For f(x) = 3x^2 - 14x, f'(x) = 6x - 14
If f'(x) = 6x - 14 = 0
=> x = 14/6
=> x = 7/3
At x = 7/3, y = -49/3
The required equation of the horizontal tangent is y = -49/3