Let be the function defined by . Consider the square region . Let be called the green region and be called the red region. Let be the horizontal line drawn at a height . Then which of the following statements is(are) true?
(A)There exists an such that the area of the green region above the line equals the area of the green region below the line
(B)There exists an such that the area of the red region above the line equals the area of the red region below the line Correct
(C)There exists an such that the area of the green region above the line equals the area of the red region below the line Correct
(D)There exists an such that the area of the red region above the line equals the area of the green region below the line Correct
Answer: (B),(C),(D)
Solution
, so red and green each have area . vanishes at ; , , , so . Let and $ =
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