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y = -6x2 - 12x - 1
We recognize this as the equation of a parabola opening downward, but we don't need to know that in order to answer the question.
At the extremes of a function (local max or min), the first derivative of the function = zero.
The first derivative of the given function with respect to 'x' is dy/dx = -12x -12
Set -12x - 12 = 0.
-x - 1 = 0
x = -1
y = -6x2 - 12x - 1 = -6(1) - 12(-1) - 1 = -6 + 12 - 1 = 5
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