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The function y=6x²+2x-8 has a horizontal tangent at _______

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Final answer:

The function y=6x²+2x-8 has a horizontal tangent at x = -1/6, which is found by setting the derivative 12x + 2 to zero and solving for x.

Step-by-step explanation:

The function y=6x²+2x-8 will have a horizontal tangent when the derivative of the function with respect to x is equal to 0. The derivative, dy/dx = 12x + 2, represents the slope of the tangent to the curve at any point x. To find the x-value(s) where the tangent is horizontal, we set the derivative equal to 0 and solve for x:

12x + 2 = 0

x = -⅖

Thus, the function y=6x²+2x-8 has a horizontal tangent at x = -⅖.

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