Question

question find the average rate of change of the function f(x), given below, from x = -1 to x = 4. f(x)=-x^3 + 5x^2 provide your answer below:

Explanation:

Step1: Calculate $f(-1)$

Substitute $x = - 1$ into $f(x)=-x^{3}+5x^{2}$.
$f(-1)=-(-1)^{3}+5\times(-1)^{2}=1 + 5=6$

Step2: Calculate $f(4)$

Substitute $x = 4$ into $f(x)=-x^{3}+5x^{2}$.
$f(4)=-(4)^{3}+5\times(4)^{2}=-64 + 80 = 16$

Step3: Apply average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-1$, $b = 4$.
$\frac{f(4)-f(-1)}{4-(-1)}=\frac{16 - 6}{4 + 1}=\frac{10}{5}=2$

Answer:

$2$