Question

for the function f(x)=2^x - x, the average rate of change for the interval 2,6 is

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$, $b = 6$, and $f(x)=2^{x}-x$.

Step2: Calculate $f(6)$

$f(6)=2^{6}-6=64 - 6=58$.

Step3: Calculate $f(2)$

$f(2)=2^{2}-2=4 - 2 = 2$.

Step4: Calculate the average rate of change

$\frac{f(6)-f(2)}{6 - 2}=\frac{58 - 2}{4}=\frac{56}{4}=14$.

Answer:

$14$