Macdonald Ramirez
09/19/2023 · Senior High School
1. Obtén los puntos máximos y mínimos de cada función, y grafica cada función. \[ \begin{array}{l}\text { (c) } f(\mathrm{x})=x^{3}-4 x^{2}-11 x+30\end{array} \]
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Para encontrar los puntos máximos y mínimos de la función \( f(x) = x^3 - 4x^2 - 11x + 30 \), calcula la derivada y los puntos críticos. La derivada es \( f'(x) = 3x^2 - 8x - 11 \). Los puntos críticos son \( x = \frac{11}{3} \) y \( x = -1 \). La segunda derivada \( f''(x) = 6x - 8 \) indica que en \( x = \frac{11}{3} \) hay un mínimo (\( f\left(\frac{11}{3}\right) = \frac{326}{27} \approx 12.07 \)) y en \( x = -1 \) hay un máximo (\( f(-1) = 36 \)). Grafica la función para visualizar estos puntos.
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