let $f(x)=x^{2}+5x - 8$. what is the average rate of change from $x = 2$ to $x = 6$? enter your answer in…
let $f(x)=x^{2}+5x - 8$. what is the average rate of change from $x = 2$ to $x = 6$? enter your answer in the box.
Answer
Explanation:
Step1: Find f(6)
Substitute x = 6 into f(x): $f(6)=6^{2}+5\times6 - 8=36 + 30-8=58$
Step2: Find f(2)
Substitute x = 2 into f(x): $f(2)=2^{2}+5\times2 - 8=4 + 10-8=6$
Step3: Calculate average rate of change
The formula for average rate of change from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$, $b = 6$. $\frac{f(6)-f(2)}{6 - 2}=\frac{58 - 6}{4}=\frac{52}{4}=13$
Answer:
13