rounded to three decimal places, find the average rate of change of the cartesian function y = f(x) on the…
rounded to three decimal places, find the average rate of change of the cartesian function y = f(x) on the interval -π/4,0, where f(x)=2cos(2x)-6. then fill in the sentence below. answer attempt 1 out of 3 average rate of change = because this is function, the average rate of change can best be thought of as between the two points.
Answer
Explanation:
Step1: Definir la fórmula de tasa de cambio promedio
La tasa de cambio promedio de una función $y = f(x)$ en el intervalo $[a,b]$ está dada por $\frac{f(b)-f(a)}{b - a}$. Aquí, $a=-\frac{\pi}{4}$ y $b = 0$, y $f(x)=2\cos(2x)-6$.
Step2: Calcular $f(0)$
Sustituir $x = 0$ en $f(x)$: $f(0)=2\cos(2\times0)-6=2\cos(0)-6=2\times1 - 6=-4$.
Step3: Calcular $f(-\frac{\pi}{4})$
Sustituir $x=-\frac{\pi}{4}$ en $f(x)$: $f(-\frac{\pi}{4})=2\cos(2\times(-\frac{\pi}{4}))-6=2\cos(-\frac{\pi}{2})-6=2\times0 - 6=-6$.
Step4: Calcular la tasa de cambio promedio
Usar la fórmula $\frac{f(b)-f(a)}{b - a}=\frac{f(0)-f(-\frac{\pi}{4})}{0-(-\frac{\pi}{4})}=\frac{-4-(-6)}{\frac{\pi}{4}}=\frac{2}{\frac{\pi}{4}}=\frac{8}{\pi}\approx2.546$.
Answer:
$2.546$