Mathematics

The shaded portion in the graph above is represented by

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