The smallest value of x^2 - 3x + 3 in the int | vedclass

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(A) Let $f(x) = x^2 - 3x + 3$. Completing the square,we get $f(x) = (x - 3/2)^2 + 3/4$. The vertex of the parabola is at $x = 3/2$. Since the interval

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$3/4$

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(A) Let $f(x) = x^2 - 3x + 3$. Completing the square,we get $f(x) = (x - 3/2)^2 + 3/4$. The vertex of the parabola is at $x = 3/2$. Since the interval is $(-3, 3/2)$,the function $f(x)$ is strictly decreasing on this interval. As $x$ approaches $3/2$ from the left,$f(x)$ approaches $3/4$. Since $3/2$ is not included in the interval,the function does not attain the value $3/4$,but it is the infimum (greatest lower bound) of the function on this interval.

The smallest value of $x^2 - 3x + 3$ in the interval $(-3, 3/2)$ is

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