Find the minimum or max value of f(x)=-x^2-2x-6. Then state the domain and range of the function.
Minimum and maximum values occur when dy/dx = 0. So differentiate the equation: f'(x) = -2x - 2. This equals to 0 at one point, which is -2x = 2, or x=-1.
Since the original equation is negative in the x^2 term, this is a maximum point. Substitute x=-1 to find the maximum value: -2(-1)^2 - 2(-1) - 6 = -6.
The domain of the function is all x for which this function can apply, that is, the real numbers.
The range of the function is all f(x) values that result from applying this function. We know it has a maximum point at f(x) = -6, so the range is -infinity to -6.
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