F(x)=-x^5+4x^3-x+1 # of turns # of solutions and is the right side going up or down?
1 answer:
Hello from MrBillDoesMath!
Answer:
See Discussion below.
Discussion:
From the attachment, f(x) has three real roots (and 2 complex roots).
As x increases, the polynomial approaches negative infinity and as x deceases it approaches positive infinity.
The attachment shows there are 3 "turning" or inflection points of f(x).
Thank you,
MrB
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9514 1404 393
Answer:
8√3 ≈ 13.86 ft
Step-by-step explanation:
The light source is usually placed at the focus, so the focus-vertex distance is p=3 ft. The equation for the parabola with its vertex at the origin is ...
y = 1/(4p)x^2
y = 1/12x^2
The opening for some y-value extends ±x from the axis of symmetry, so is a total of 2x in width.
For y=4, the corresponding value of x is ...
4 = 1/12x^2
48 = x^2
√48 = x = 4√3
Then the width of the searchlight opening is ...
2(4√3 ft) = 8√3 ft ≈ 13.86 ft
