The shaded portion in the graph above is represented by
-
A.
y + x – x3 ≥ 0, y – x ≤ 0 -
B.
y – x + x3 ≥ 0, y – x ≤ 0 -
C.
y + x – x3 ≤ 0, y + x ≥ 0 -
D.
y – x + x3 ≤ 0, y + x ≥ 0
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