Question

Find the average rate of change for problems 1-3: X. X^2+7 2. 11 3. 16 4. 23 5. 32 6. 43 1) what is the average rate of change between x=2 and x=5 2) what is the average rate of change between x=3 and x=6 3) what is the average rate of change between x=2 and x=4

Answer 1

Answer:

(1)7 (2)9 (3)6

Step-by-step explanation:

$\left|\begin{array}{c|cc}X&f(X)=X^2+7\\--&-----\\2&11\\3&16\\4&23\\5&32\\6&43\end{array}\right|$

(1)The average rate of change between x=2 and x=5

$\dfrac{dy}{dx} =\dfrac{f(5)-f(2)}{5-2} =\dfrac{32-11}{3} =\dfrac{21}{3} =7$

(2)The average rate of change between x=3 and x=6

$\dfrac{dy}{dx} =\dfrac{f(6)-f(3)}{6-3} =\dfrac{43-16}{3} =\dfrac{27}{3} =9$

(3)The average rate of change between x=2 and x=4

$\dfrac{dy}{dx} =\dfrac{f(4)-f(2)}{4-2} =\dfrac{23-11}{2} =\dfrac{12}{2} =6$