Prove that the function f defined by f(x) = x^2 - x +1 is neither increasing nor decreasing in (- 1, 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.
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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).
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