What is the equation of the horizontal tangent to the curve y = 3x^2 - 14x

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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

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