Prove that the function f given by f (x) = x² – x + 1 is neither strictly increasing nor strictly decreasing on (– 1, 1).

It is given that function f(x) = x² – x + 1

f’(x) = 2x – 1

If f’(x) = 0, then we get,

⇒ x =

So, the point x = divides the interval (-1,1) into two disjoint intervals,

So, in interval

f’(x) = 2x – 1 < 0

Therefore, the given function (f) is strictly decreasing in interval

So, in interval

f’(x) = 2x -1 > 0

Therefore, the given function (f) is strictly increasing in interval for.

Therefore, f is neither strictly increasing and decreasing in interval (-1,1).