the function given by y = f(x) shows the average monthly temperature (°f) for lisbon. the value of x is the…

the function given by y = f(x) shows the average monthly temperature (°f) for lisbon. the value of x is the month number and x = 1 represents january. average monthly temperature for lisbon part 1 of 2 (a) find the average rate of change in temperature between months 3 and 5 (march and may). the average rate of change in temperature between months 3 and 5 (march and may) is °f/month. part 2 of 2 (b) find the average rate of change in temperature between months 9 and 11 (september and november). the average rate of change in temperature between months 9 and 11 (september and november) is °f/month.

the function given by y = f(x) shows the average monthly temperature (°f) for lisbon. the value of x is the month number and x = 1 represents january. average monthly temperature for lisbon part 1 of 2 (a) find the average rate of change in temperature between months 3 and 5 (march and may). the average rate of change in temperature between months 3 and 5 (march and may) is °f/month. part 2 of 2 (b) find the average rate of change in temperature between months 9 and 11 (september and november). the average rate of change in temperature between months 9 and 11 (september and november) is °f/month.

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$.

Step2: Solve part (a)

For the interval from $x = 3$ to $x = 5$, we know that $f(3)=59$ and $f(5)=64$. Using the formula $\frac{f(5)-f(3)}{5 - 3}=\frac{64 - 59}{2}=\frac{5}{2}=2.5$.

Step3: Solve part (b)

For the interval from $x = 9$ to $x = 11$, we know that $f(9)=72$ and $f(11)=59$. Using the formula $\frac{f(11)-f(9)}{11 - 9}=\frac{59 - 72}{2}=\frac{- 13}{2}=-6.5$.

Answer:

(a) $2.5$ (b) $-6.5$