The shaded portion in the graph above is represented by
-
y + x - x3 ≥ 0, y - x ≤ 0
- y - x + x3 ≥ 0, y - x ≤ 0
- y + x - x3 ≤ 0, y + x ≥ 0
- y - x + x3 ≤ 0, y + x ≥ 0
The correct answer is: A
Explanation
y + x - x2 ≥ 0y = x3 - x
on x axis, y = 0
∴x2 - x = 0
x(x2 - 1) = 0
x = 0 or x2 - 1 = 0
x2 = 1
x = +/-1
∴ x = -1, 0 and 1 which are the roots of the equation y + x - x2 ≥ 0
Also y - x ≤ 0
=> y ≤ 0 + x
∴ the region where y ≤ 0