find the average rate of change for f(x) = x² - 3x - 10 from x = 4 to x = 6.\na 5\nb 7\nc 9\nd 11
find the average rate of change for f(x) = x² - 3x - 10 from x = 4 to x = 6.\na 5\nb 7\nc 9\nd 11
Answer
Explanation:
Step1: Calculate f(4)
Substitute x = 4 into f(x): $f(4)=4^{2}-3\times4 - 10=16 - 12-10=-6$
Step2: Calculate f(6)
Substitute x = 6 into f(x): $f(6)=6^{2}-3\times6 - 10=36-18 - 10=8$
Step3: Use average rate of change formula
The average rate of change of a function from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 4$, $b = 6$. $\frac{f(6)-f(4)}{6 - 4}=\frac{8-(-6)}{2}=\frac{8 + 6}{2}=\frac{14}{2}=7$
Answer:
B. 7