+0  
 
0
95
1
avatar+142 

For what values of x is

\(\frac{x-10x^2+25x^3}{8-x^3}\)

nonnegative. Ansewr as an interval.

DanielCai  Jun 28, 2018
 #1
avatar+88898 
+2

(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 

 

 

 

cool cool cool

CPhill  Jun 28, 2018

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