In the interval [0, 1], the function x2 – x + 1 is

1) Increasing

2) Decreasing

3) Neither increasing nor Decreasing

4) None of the above

Solution: (3) Neither increasing or Decreasing

f (x) = x2 – x + 1

x ∈ (-1, 1)

f’ (x) = 2x – 1

Put f’ (x) = 0

2x – 1 = 0

2x = 1

x = 1 / 2

The point x = 1 / 2 divides the intervals (-1, 1) into 2 disjoint intervals. (-1, 1 / 2) and (1 / 2, 1).

f (x) is neither decreasing nor increasing on (-1, 1).

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