Dawson Patel
06/30/2024 · Middle School
\( \left. \begin{array} { l } { f ( x ) = - x ^ { 3 } + 6 x ^ { 2 } - 9 x + 11 } \\ { [ - 3,7 , - 30,30 ] } \end{array} \right. \)
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The function \( f(x) = -x^3 + 6x^2 - 9x + 11 \) has critical points at \( x = 1 \) and \( x = 3 \). Evaluating the function at these points and the endpoints of the interval \( [-3, 7] \) gives \( f(-3) = 119 \), \( f(1) = 7 \), \( f(3) = 11 \), and \( f(7) = -101 \). The maximum value is 119 at \( x = -3 \) and the minimum value is -101 at \( x = 7 \).
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