Question

what is the average rate of change of the function $f(x)=4x^{2}+3x$ on the interval $1,5$? the average rate of change is

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$, $b = 5$, and $f(x)=4x^{2}+3x$.

Step2: Calculate $f(5)$

Substitute $x = 5$ into $f(x)$: $f(5)=4\times5^{2}+3\times5=4\times25 + 15=100 + 15=115$.

Step3: Calculate $f(1)$

Substitute $x = 1$ into $f(x)$: $f(1)=4\times1^{2}+3\times1=4 + 3=7$.

Step4: Calculate the average rate of change

Using the formula $\frac{f(b)-f(a)}{b - a}$, we have $\frac{f(5)-f(1)}{5 - 1}=\frac{115 - 7}{4}=\frac{108}{4}=27$.

Answer:

$27$