AYUDAAAAAA! FUNCIONES Sea : f : R⇒R / f(x) = y = 13( [tex] \ frac{x}{16x ^ {2} + 9} [ / tex] ) + 12( [tex] \ frac{1}{16x + 9x ^ { - 1}} [ / tex] ) Hallar un valor de m > 0 para f(x), tal que |f(x)| ≤ M ∀ x ∈ Dominiof 45 ptos a quien me responda de forma detallada y bien explicado.
En resumen
<img src="https://tex.z-dn.net/?
<img src="https://tex.z-dn.net/?f=%20f%28x%29%3D%5Cdfrac%7B13x%7D%7B16x%5E2%2B9%7D%2B%5Cdfrac%7B12%7D%7B16x%2Bx%5E%7B-1%7D%7D%5C%5C%20%5C%5C%20%5C%5C%20F%28x%29%3D%5Cdfrac%7B13x%7D%7B16x%5E2%2B9%7D%2B%5Cdfrac%7B12x%7D%7B16x%5E2%2B9%7D%5C%5C%20%5C%5C%20%5C%5C%20F%28x%29%3D%5Cdfrac%7B25x%7D%7B16x%5E2%2B9%7D%5C%5C%20%5C%5C%20%5C%5C%20%5Ctext%7BHallemos%20el%20valor%20donde%20%24F%24%20se%20hace%20m%5C%27inimo%2C%20para%20ello%20encontremos%20los%20%7D%5C%5C%20%5Ctext%7Bpuntos%20cr%5C%27iticos%7D%5C%5C%20%5C%5C%20%5Cdfrac%7BdF%7D%7Bdx%7D%3D0%5C%5C%20%5C%5C%20%5C%5C%20%5Cdfrac%7B25%2816x%5E2%2B9%29-32x%2825x%29%7D%7B%2816x%5E2%2B9%29%5E2%7D%3D0%5C%5C%20%5C%5C%20%5C%5C%20%5Cdfrac%7B9-16x%5E2%7D%7B%2816x%5E2%2B9%29%5E2%7D%3D0%5C%5C%20%5C%5C%20%5C%5C%209-16x%5E2%3D0%5C%5C%20%5C%5C%20%5Cboxed%7Bx%3D%5Cpm%5Cdfrac%7B3%7D%7B4%7D%7D%20%20" />
<img src="https://tex.z-dn.net/?f=%20%5Ctext%7BAhora%20comprobemos%20si%20tal%20punto%20es%20un%20extremo%7D%5C%5C%20%5C%5C%20%5Cdfrac%7Bd%5E2F%7D%7Bdx%5E2%7D%3D%5Cdfrac%7B32x%2816x%5E2-27%29%7D%7B%2816x%5E2%2B9%29%5E3%7D%5C%5C%20%5C%5C%20%5C%5C%20F%27%27%28-3%2F4%29%3D2%2F27%5Cto%20x%3D-%5Cdfrac%7B3%7D%7B4%7D%5Ctext%7B%20es%20punto%20de%20m%5C%27inimo%7D%5C%5C%20%5C%5C%20%5C%5C%20F%27%27%283%2F4%29%3D-2%2F27%5Cto%20x%3D%5Cdfrac%7B3%7D%7B4%7D%5Ctext%7B%20es%20punto%20de%20m%5C%27aximo%7D%5C%5C%20%5C%5C%20%5C%5C%20%5Ctext%7BEntonces%20%7D%5C%5C%20%5C%5C%20F_%7Bmin%7D%3DF%28-3%2F4%29%3D-25%2F24%5C%5C%20%5C%5C%20F_%7Bmax%7D%3DF%283%2F4%29%3D25%2F24%5C%5C%20%5C%5C%20%5C%5C%20%5Ctext%7BEs%20decir%2C%20%24%5Cforall%20x%5Cin%20%5Cmathbb%7BR%7D%5C%2C%2C%5C%2C%20-%5Cdfrac%7B25%7D%7B4%7D%5Cleq%20F%28x%29%5Cleq%5Cdfrac%7B25%7D%7B24%7D%20%5Ciff%20%7CF%28x%29%7C%5Cleq%20%5Cdfrac%7B25%7D%7B24%7D%24%20%7D%20" />
<img src="https://tex.z-dn.net/?f=%20%5Ctextbf%7BObservaci%5C%27on%3A%20%7D%5Ctext%7Blas%20funciones%20%24f%24%20y%20%24F%24%20son%20equivalentes%20salvo%20cuando%20%24x%3D0%24%7D%20" />
Por ende <img src="https://tex.z-dn.net/?f=%20f%28x%29%3DF%28x%29%2C%5Cforall%20x%5Cin%20Dom%28f%29%20%20" /> , así M = 25 / 24.
Si a x a x a = 2160 a³ = 2160 ³√a = ³√2160 a = 12 Hallar a² - 4a + 7 = 12² - 4(12) + 7 = 144 - 48 + 7 = 103.
Como son funciones lineales bastaran dos puntos, para hallar sus gráficas, entonces : .