Question 608072
f(x)=2-2x^2
Estimate the intervals on which the function is increasing or decreasing and estimate any relative maxima or minima. Thanks and could you also show work
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This is a "quadratic" because it is a polynomial of degree 2.
Because it's a quadratic, it is a parabola.
We know the parabola opens downward because the coefficient associated with the x^2 term is negative (think sad face).
Since it is a parabola that opens downwards, we know the vertex is at the MAXIMUM.
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Axis of symmetry:
x = -b/(2a)
x = -0/(2(-2))
x = -0/(-4)
x = 0
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Increasing interval:
(-oo, 0)
Decreasing interval:
(0, +oo)
where oo is for infinity
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Maximum:
f(0)=2-2(0)^2
f(0)=2
so, max is at (0,2)