Prove that the function f defined by f(x) = x2 - x +1 is neither in

1.	Prove that the function f defined by f(x) = x2 - x +1 is neither increasing nor decreasing in (- 1, 1). Hence find the intervals in which f(x) is : (i) strictly increasing(ii) strictly decreasing.
Answer» f'(x) = 2x - 1 f'(x) > 0, ∀ x ∈ (1/2 ,1) f'(x) < 0 , ∀ x ∈ (-1, 1/2) . ^.. f(x) is neither increasing nor decreasing in (-1, 1) f(x) is strictly increasing on (1/2 , 1) and f(x) is strictly decreasing on (-1, 1/2).

Prove that the function f defined by f(x) = x2 - x +1 is neither increasing nor decreasing in (- 1, 1). Hence find the intervals in which f(x) is : (i) strictly increasing(ii) strictly decreasing.

Answer»

f'(x) = 2x - 1

f'(x) > 0, ∀ x ∈ (1/2 ,1)

f'(x) < 0 , ∀ x ∈ (-1, 1/2)

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

f(x) is strictly increasing on (1/2 , 1)

and f(x) is strictly decreasing on (-1, 1/2).