What is -x^3+x^2-2x>= 0 ?

The solution to -x^3+x^2-2x>= 0 is x<= 0

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-x^3+x^2-2x>= 0

- x^{3} + x^{2} - 2 x \geq 0

x \leq 0

Interval Notation

(- \infty, 0]

Solution steps

- x^{3} + x^{2} - 2 x \geq 0

Factor

- x^{3} + x^{2} - 2 x : - x (x^{2} - x + 2)

- x (x^{2} - x + 2) \geq 0

Multiply both sides by

- 1

(reverse the inequality)

(- x (x^{2} - x + 2)) (- 1) \leq 0 \cdot (- 1)

Simplify

x (x^{2} - x + 2) \leq 0

Identify the intervals

x \leq 0

(x + 1) (x + 6) < 0

\frac{1}{( x - 1 )} > 0

\frac{( - x ^{2} + 4 x - 3 )}{( 2 x - 8 )} > 0

\frac{2 x - x ^{2}}{( 3 + x ) \cdot ( 5 - x )} < 0

x^{2} \cdot (x + 2) < 0