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For the function f(x) = x^(1/3)(x - 1), which of the following statements is TRUE?

1. the area of the region enclosed by the curve in the fourth quadrant is 9/28
2. it is strictly increasing for x > 1/4 and strictly decreasing for x < 1/4
3. it is concave down on (-1/2, 0)
4. it has exactly two points of inflection

Correct answer: the area of the region enclosed by the curve in the fourth quadrant is 9/28

Solution

On 0 < x < 1 the function is negative (fourth quadrant); integrating gives 3/7 - 3/4 = -9/28, so the enclosed area is 9/28.

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