The shaded portion in the graph above is represented by
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Correct Answer: Option A
Explanation:
y + x - x2 ≥ 0
y = 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
y + x - x2 ≥ 0
y = 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