exam 1 (chapters 1-3) score: 30/100 answered: 7/20 question 1 find the average rate of change of g(x)=5x³ +…
exam 1 (chapters 1-3) score: 30/100 answered: 7/20 question 1 find the average rate of change of g(x)=5x³ + 1 from x = -3 to x = 2.
Answer
Explanation:
Step1: Recall average - rate - of - change formula
The average rate of change of a function $y = g(x)$ from $x=a$ to $x = b$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a=-3$, $b = 2$, and $g(x)=5x^{3}+1$.
Step2: Calculate $g(-3)$
Substitute $x=-3$ into $g(x)$: $g(-3)=5\times(-3)^{3}+1=5\times(-27)+1=-135 + 1=-134$.
Step3: Calculate $g(2)$
Substitute $x = 2$ into $g(x)$: $g(2)=5\times2^{3}+1=5\times8+1=40 + 1=41$.
Step4: Calculate the average rate of change
$\frac{g(2)-g(-3)}{2-(-3)}=\frac{41-(-134)}{2 + 3}=\frac{41 + 134}{5}=\frac{175}{5}=35$.
Answer:
35