Question

find the average rate of change of ( f(x) = 2x^2 - 7x ) from ( x = 1 ) to ( x = 6 ).
simplify your answer as much as possible.

Explanation:

Step1: Recall average rate formula

The average rate of change of a function $f(x)$ from $x=a$ to $x=b$ is $\frac{f(b)-f(a)}{b-a}$.

Step2: Calculate $f(6)$

$f(6)=2(6)^2 -7(6)=2(36)-42=72-42=30$

Step3: Calculate $f(1)$

$f(1)=2(1)^2 -7(1)=2-7=-5$

Step4: Compute rate of change

$\frac{f(6)-f(1)}{6-1}=\frac{30-(-5)}{5}=\frac{35}{5}=7$

Answer:

7