find the average rate of change of the function as x changes from a to b. f(x)=2x³; a = -3, b = 4 what is…
find the average rate of change of the function as x changes from a to b. f(x)=2x³; a = -3, b = 4 what is the average rate of change? (type an integer or a simplified fraction.)
Answer
Explanation:
Step1: Recall the average - rate - of - change formula
The average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$.
Step2: Calculate $f(a)$ and $f(b)$
Given $f(x)=2x^{3}$, when $a=-3$, $f(a)=2\times(-3)^{3}=2\times(-27)=-54$. When $b = 4$, $f(b)=2\times4^{3}=2\times64 = 128$.
Step3: Substitute into the formula
$\frac{f(b)-f(a)}{b - a}=\frac{128-(-54)}{4-(-3)}=\frac{128 + 54}{4 + 3}=\frac{182}{7}=26$.
Answer:
26