In which interval is the function f(x) = x^2 | vedclass

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(C) Given the function $f(x) = x^2 - x + 1$.First,find the derivative: $f'(x) = 2x - 1$.For the function to be monotonic,$f'(x)$ must be either non-ne

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$(0, 1)$

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(C) Given the function $f(x) = x^2 - x + 1$.First,find the derivative: $f'(x) = 2x - 1$.For the function to be monotonic,$f'(x)$ must be either non-negative $(f'(x) \ge 0)$ or non-positive $(f'(x) \le 0)$ throughout the interval.Setting $f'(x) = 0$,we get $2x - 1 = 0$,which implies $x = 1/2$.For $x For $x > 1/2$,$f'(x) > 0$ (the function is strictly increasing).In any interval that contains $x = 1/2$ in its interior,such as $(0, 1)$,the derivative changes sign. Therefore,the function is not monotonic in any interval containing $1/2$ as an interior point.

In which interval is the function $f(x) = x^2 - x + 1$ not monotonic?

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