Question

Given the function g(x) x2 + 10x + 20,determine the average rate of change of thefunction over the interval -9 < x < 0.

Answer 1

Step 1: Given the equation

$g(x)=x^2+10x+20$

Step 2: Evaluate g(-9).

$\begin{gathered} g(-9)=(-9)^2+10(-9)+20 \\ =81-90+20=11 \end{gathered}$

Step 3: Evaluate g(0)

$\begin{gathered} g(0)=0^2+10(0)+20 \\ =20 \end{gathered}$

Step 4: Given an interval [-9 , 0], the rate of change formula is

$\begin{gathered} \text{Rate of change(R) = }\frac{g(0)-g(-9)}{0-(-9)} \\ \end{gathered}$

Step 5: Substitute for the values of g(0) and g(-9)

$\begin{gathered} R=\frac{20-11}{0+9} \\ =\frac{9}{9}=1 \end{gathered}$

Therefore, the average rate of change for the function over the interval [-9,0] is 1