Calcula la tasa de variacion media de la función f(x) = - 2x + 5 en los intervalos [ - 5, - 3], [3, 5] y [10, 20]?

PREGUNTA Calcula la tasa de variacion media de la función f(x) = - 2x + 5 en los intervalos [ - 5, - 3], [3, 5] y [10, 20]

SOLUCIÓN

Hola!

: D

Recordemos que la tasa de variación media está dado por <img src="https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboldsymbol%7B%5Cmathrm%7BTVM%28a%2Cb%29%20%3D%20%5Cdfrac%7Bf%28b%29%20-%20f%28a%29%7D%7Bb%20-%20a%7D%20%7D%7D%7D%2C%20siendo%20%5C%3A%20a%3Cb" />

En el ejercicio

Para [ - 5 , - 3] <img src="https://tex.z-dn.net/?f=TVM%28-5%2C-3%29%20%3D%20%5Cdfrac%7Bf%28-3%29%20-%20f%28-5%29%7D%7B-3%20-%20%28-5%29%7D%20%5C%5C%5C%5CTVM%28-5%2C-3%29%20%3D%20%5Cdfrac%7B%5B-2%28-3%29%2B5%5D-%5B-2%28-5%29%2B5%5D%7D%7B2%7D%5C%5C%20%5C%5CTVM%28-5%2C-3%29%20%3D%20%5Cdfrac%7B11-15%7D%7B2%7D%5C%5C%5C%5CTVM%28-5%2C-3%29%20%3D%20%5Cdfrac%7B-4%7D%7B2%7D%5C%5C%5C%5CTVM%28-5%2C-3%29%20%3D%20-2" />

Para [3, 5] <img src="https://tex.z-dn.net/?f=TVM%283%2C5%29%20%3D%20%5Cdfrac%7Bf%285%29%20-%20f%283%29%7D%7B5%20-%203%7D%20%5C%5C%5C%5CTVM%283%2C5%29%20%3D%20%5Cdfrac%7B%5B-2%285%29%2B5%5D-%5B-2%283%29%2B5%5D%7D%7B2%7D%5C%5C%20%5C%5CTVM%283%2C5%29%20%3D%20%5Cdfrac%7B-5-%28-1%29%7D%7B2%7D%5C%5C%5C%5CTVM%283%2C5%29%20%3D%20%5Cdfrac%7B-4%7D%7B2%7D%5C%5C%5C%5CTVM%283%2C5%29%20%3D%20-2" />

Para [10, 20] <img src="https://tex.z-dn.net/?f=TVM%2810%2C20%29%20%3D%20%5Cdfrac%7Bf%2820%29%20-%20f%2810%29%7D%7B20%20-%2010%7D%20%5C%5C%5C%5CTVM%2810%2C20%29%20%3D%20%5Cdfrac%7B%5B-2%2820%29%2B5%5D-%5B-2%2810%29%2B5%5D%7D%7B10%7D%5C%5C%5C%5C%20TVM%2810%2C20%29%20%3D%20%5Cdfrac%7B-35-%28-15%29%7D%7B10%7D%5C%5C%5C%5C%20TVM%283%2C5%29%20%3D%20%5Cdfrac%7B-20%7D%7B10%7D%5C%5C%5C%5CTVM%283%2C5%29%20%3D%20-2" />.