+145 For what values of x is
\(\frac{x-10x^2+25x^3}{8-x^3}\)
nonnegative. Ansewr as an interval.
+129852 (25x^3 - 10x^2 + x )
_______________ ≥ 0
8 - x^3
x ( 25x^2 - 10x + 1)
________________ ≥ 0
(2 - x) ( x^2 + 2x + 4)
x ( 5x -1) ( 5x - 1)
_________________ ≥ 0
(2 - x) (x^2 + 2x + 4)
x (5x - 1)^2
________________ ≥ 0
(2 - x)(x^2 + 2x + 4)
Note that (5x - 1)^2 is ≥ 0 for all x and ( x^2 + 2x + 4) is > 0 for all x
So we only need consider what x values makes
x
_____ ≥ 0
2 - x
Note that if x is negative...the function is negative
And if x > 2, the function is negative
So...the x values that make this ≥ 0 are 0 ≤ x < 2
