Answer:
-9
Step-by-step explanation:
Given function:
[tex]f(x)=-9x+4[/tex]
Given x-values:
Calculate the value of the function for the two given values of x:
[tex]\begin{aligned}\implies f(x_1)&=-9(-5)+4\\&=45+4\\&=49\end{aligned}[/tex]
[tex]\begin{aligned}\implies f(x_2)&=-9(0)+4\\&=0+4\\&=4\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Average rate of change of function $f(x)$}\\\\$\dfrac{f(b)-f(a)}{b-a}$\\\\over the interval $a \leq x \leq b$\\\end{minipage}}[/tex]
As -5 < 0:
Therefore:
[tex]\begin{aligned} \implies \textsf{Average rate of change}&=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}\\\\&=\dfrac{4-49}{0-(-5)}\\\\&=\dfrac{-45}{5}\\\\&=-9\end{aligned}[/tex]
