Mccoy Morrison
09/20/2024 · Elementary School
función \( f \) se define asi: \( f(x)=\cos ^{2} x-3 \operatorname{sen}^{2} x, 0 \leq x \leq \pi \). Halle las raices de la ecuación \( f(x)=0 \). (i) Halle \( f^{\prime}(x) \). (ii) A partir de lo anterior, halle las coordenadas de los puntos del gráfico de \( y=f(x) \) en los que \( f^{\prime}(x)=0 \).
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Para encontrar las raíces de \( f(x) = 0 \), primero calculamos la derivada \( f^{\prime}(x) \) y luego hallamos los puntos donde \( f^{\prime}(x) = 0 \). Los puntos donde \( f^{\prime}(x) = 0 \) son \( x = 0, \frac{\pi}{2}, \pi \), y sus coordenadas en el gráfico de \( y = f(x) \) son \( (0, 1), \left(\frac{\pi}{2}, -3\right), (\pi, 1) \).
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