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.